Integrable theory of the perturbation equations.

From MaRDI portal
Publication:815580

DOI10.1016/0960-0779(95)00104-2zbMath1080.37578arXivsolv-int/9604004OpenAlexW3102905151MaRDI QIDQ815580

Benno Fuchssteiner, Wen-Xiu Ma

Publication date: 17 February 2006

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9604004



Related Items

A nonlinear integrable couplings of C-KdV soliton hierarchy and its infinite conservation laws, Bi-integrable couplings of a new soliton hierarchy associated with \(\mathrm{SO}(4)\), Bi-integrable couplings of a new soliton hierarchy associated with a non-semisimple Lie algebra, Integrable counterparts of the D-Kaup-Newell soliton hierarchy, Invariant solutions for a class of perturbed nonlinear wave equations, Riemann-Hilbert problems and \(N\)-soliton solutions for a coupled mKdV system, Self-consistent sources and conservation laws for a super Broer-Kaup-Kupershmidt equation hierarchy, Self-consistent sources and conservation laws for nonlinear integrable couplings of the Li soliton hierarchy, Continuous limits for an integrable coupling of the Kac-Van Moerbeke hierarchy, The integrable couplings of the modified Jaulent-Miodek hierarchy and its Hamiltonian structure, Application of a semi-direct sum of Lie algebras to the TD hierarchy, A new Lie algebra and soliton solutions, Bäcklund transformation of soliton equations, Hamiltonian and super-Hamiltonian systems of a hierarchy of soliton equations, A new hierarchy of integrable system of \(1+2\) dimensions: from Newton's law to generalized Hamiltonian system. II., An approach for generating enlarging integrable systems, Constructing nonlinear discrete integrable Hamiltonian couplings, Variational identities and applications to Hamiltonian structures of soliton equations, Approximate solution of the Kuramoto-Shivashinsky equation on an unbounded domain, A soliton hierarchy associated with \(\mathrm{so}(3,\mathbb R)\), An integrable lattice hierarchy, associated integrable coupling, Darboux transformation and conservation laws, Integrable coupling hierarchy and Hamiltonian structure for a matrix spectral problem with arbitrary-order, Three nonlinear integrable couplings of the nonlinear Schrödinger equations, A real nonlinear integrable couplings of continuous soliton hierarchy and its Hamiltonian structure, An integrable couplings of G-WKI equations hierarchy with self-consistent sources, The multicomponent discrete equation hierarchy with variable spectral parameters and a new integrable coupling system, A new method to construct the integrable coupling system for discrete soliton equation with the Kronecker product, A hierarchy of Liouville integrable discrete Hamiltonian equations, Two hierarchies of integrable lattice equations associated with a discrete matrix spectral problem, Integrable couplings of the hierarchies of evolution equations., Non-isospectral integrable couplings of Ablowitz-Ladik hierarchy with self-consistent sources, Riemann-Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions, A complex integrable hierarchy and its Hamiltonian structure for integrable couplings of WKI soliton hierarchy, Conservation laws and self-consistent sources for an integrable lattice hierarchy associated with a three-by-three discrete matrix spectral problem, The semidirect sum of Lie algebras and its applications to C-KdV hierarchy, Bilinear forms and Bäcklund transformations of the perturbation systems, Tri-integrable couplings of the Giachetti-Johnson soliton hierarchy as well as their Hamiltonian structure, Nonlinear integrable couplings of Levi hierarchy and WKI hierarchy, Two expanding integrable models of the Geng-Cao hierarchy, Integrable couplings of the Burgers hierarchy and its Hamiltonian structure as well as its solutions, A type of new integrable Hamiltonian hierarchy and expanding integrable model of its reduced integrable system associated with a new loop algebra, Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies, A hierarchy of Hamiltonian lattice equations associated with the relativistic Toda type system, A hierarchy of nonlinear lattice soliton equations, its integrable coupling systems and infinitely many conservation laws, An \(\mathrm{so}(3,\mathbb R)\) counterpart of the Dirac soliton hierarchy and its bi-integrable couplings, Integrable coupling of the Ablowitz-Ladik hierarchy and its Hamiltonian structure, The coupling integrable couplings of the generalized coupled Burgers equation hierarchy and its Hamiltonian structure, A few expanding Lie algebras of the Lie algebra \(A_1\) and applications, A higher-dimensional Lie algebra and its decomposed subalgebras, An unified form of the AKNS and BPT hierarchies with two arbitrary parameters, A Liouville integrable hierarchy, symmetry constraint, new finite-dimensional integrable systems, involutive solution and expanding integrable models, A new discrete integrable system and its discrete integrable coupling system, A new loop algebra \(\tilde A_5\) and its applications to integrable system, Two integrable couplings of the Tu hierarchy and their Hamiltonian structures, Integrable systems with \(\mathrm{BMS}_{3}\) Poisson structure and the dynamics of locally flat spacetimes, Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations, Expansion of the Lie algebras and integrable couplings, A new multi-component hierarchy and its integrable expanding model, An isospectral transformation and the related integrable hierarchies of soliton equations, Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with \(\mathrm{SO}(4)\), An integrable coupling hierarchy of the MKdV\_integrable systems, its Hamiltonian structure and corresponding nonisospectral integrable hierarchy, Nonlinear continuous integrable Hamiltonian couplings, The integrable coupling system of a \(3 \times 3\) discrete matrix spectral problem, Two families of Liouville integrable lattice equations, A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems, Semi-direct sums of Lie algebras and continuous integrable couplings, A few Lie algebras and their applications for generating integrable hierarchies of evolution types, The binary nonlinearization of generalized Toda hierarchy by a special choice of parameters, Multi-component bi-Hamiltonian Dirac integrable equations, The applications of a higher-dimensional Lie algebra and its decomposed subalgebras, Three semi-direct sum Lie algebras and three discrete integrable couplings associated with the modified K dv lattice equation, A discrete iso-spectral problem with positive and negative hierarchies and integrable coupling system, A Hamiltonian structure associated with a matrix spectral problem of arbitrary-order, Hamiltonian systems and its integrable coupling associated with a new discrete spectral problem, New block matrix spectral problem and Hamiltonian structure of the discrete integrable coupling system, A new soliton hierarchy and its two extending integrable models, A new loop algebra and its expanded loop algebras, as well as their applications, Two expanding integrable systems of the GI soliton hierarchy and a generalized GI hierarchy with self-consistent sources as well as its extension form, A few new higher-dimensional Lie algebras and two types of coupling integrable couplings of the AKNS hierarchy and the KN hierarchy, Two super-integrable hierarchies and their super-Hamiltonian structures, Integrable couplings of the \((2 + 1)\)-dimensional dispersive long wave hierarchy and its Hamiltonian structure, Two expanding integrable systems and quasi-Hamiltonian function associated with an equation hierarchy, Expanding integrable models of the nonlinear Schrödinger equation, A new Lie algebra along with its induced Lie algebra and associated with applications, A hierarchy of Liouville integrable lattice equations and its integrable coupling systems, The coupling integrable couplings of the modified Korteweg-de Vries (mKdV) hierarchy, Component-trace identity for Hamiltonian structure of the integrable couplings of the giachetti-johnson (GJ) hierarchy and coupling integrable couplings, Invertible linear transformations and the Lie algebras, A hierarchy of differential-difference equations, conservation laws and new integrable coupling system, New extended Lie algebra and the generalized integrable Liouville hierarchy, A new fractional order soliton equation hierarchy and its integrable coupling system, Solving an integrable coupling system of Merola-Ragnisco-Tu lattice equation by Darboux transformation of Lax pair, Bi-integrable couplings of a Kaup-Newell type soliton hierarchy and their bi-Hamiltonian structures, Hierarchies, integrable decompositions and conservation laws of Geng equation, A non-isospectral integrable couplings of Volterra lattice hierarchy with self-consistent sources, An integrable couplings of Dirac soliton hierarchy with self-consistent sources, An integrable coupling family of Merola-Ragnisco-Tu lattice systems, its Hamiltonian structure and related nonisospectral integrable lattice family, The algebraic structure of discrete zero curvature equations associated with integrable couplings and application to enlarged Volterra systems, Integrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy, A generalized cubic Volterra lattice hierarchy and its integrable couplings system, Binary nonlinearization of spectral problems of the perturbation AKNS systems., A unified expressing model of the AKNS hierarchy and the KN hierarchy, as well as its integrable coupling system, A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system, A new subalgebra of the Lie algebra \(A_{2}\) and two types of integrable Hamiltonian hierarchies, expanding integrable models, A trick loop algebra and a corresponding Liouville integrable hierarchy of evolution equations, (2+1)-DIMENSIONAL TD HIERARCHY AND ITS INTEGRABLE COUPLINGS, INTEGRABLE COUPLINGS OF THE TC HIERARCHY AND ITS HAMILTONIAN STRUCTURE, An integrable extension of a soliton hierarchy associated with so(3,ℝ) and its bi-Hamiltonian formulation, Riemann-Hilbert problems of a six-component mKdV system and its soliton solutions, The quadratic-form identity for constructing the Hamiltonian structures of the discrete integrable systems, Liouville integrability of perturbation systems of finite-dimensional integrable Hamiltonian systems, A KIND OF NEW CONTINUOUS LIMITS OF AN INTEGRABLE COUPLING SYSTEM FOR DISCRETE AKNS HIERARCHY, The generalized fractional trace variational identity and fractional integrable couplings of Kaup-Newell hierarchy, New lattice equation hierarchies and Darboux transformation, Fractional isospectral and non-isospectral AKNS hierarchies and their analytic methods for \(N\)-fractal solutions with Mittag-Leffler functions, A new integrable symplectic map by the binary nonlinearization to the super AKNS system, Long-time asymptotics of a three-component coupled nonlinear Schrödinger system, SUBALGEBRAS OF THE LIE ALGEBRA R6AND THEIR APPLICATIONS, Upper Triangular Matrix of Lie Algebra and a New Discrete Integrable Coupling System, A type of loop algebra and the associated loop algebras, Nonlinear bi-integrable couplings of multicomponent Guo hierarchy with self-consistent sources, Travelling waves and conservation laws of a \((2+1)\)-dimensional coupling system with Korteweg-de Vries equation, Integrable couplings of the generalized Vakhnenko equation: multiple soliton solutions, A Liouville integrable lattice soliton equation, infinitely many conservation laws and integrable coupling systems, INTEGRABLE COUPLINGS OF THE (2+1)-DIMENSIONAL Li HIERARCHY AND ITS HAMILTONIAN STRUCTURE AS WELL AS THE MULTI-COMPONENT Li HIERARCHY, Two types of multicomponent matrix loop algebras and its application, A PERTURBATIVE APPROACH TO A CLASS OF FOKKER–PLANCK EQUATIONS, Bi-integrable couplings of a nonsemisimple Lie algebra by Toda lattice hierarchy, CONSTRUCTING INTEGRABLE COUPLINGS FOR THE C-KdV HIERARCHY, Nonlinear bi-integrable couplings with Hamiltonian structures, INTEGRABLE COUPLINGS OF MULTI-COMPONENT AKNS–KAUP–NEWELL EQUATIONS HIERARCHIES, A HIERARCHY OF HAMILTONIAN EQUATIONS ASSOCIATED WITH THE MODIFIED JAULENT–MIODEK HIERARCHY, Component-trace identities for Hamiltonian structures, A new Lie algebra to the multi-component Toda hierarchy and its discrete integrable coupling system, A kind of generalized integrable couplings and their bi-Hamiltonian structure, TWO FAMILIES GENERALIZATION OF AKNS HIERARCHIES AND THEIR HAMILTONIAN STRUCTURES, A LIOUVILLE INTEGRABLE MULTI-COMPONENT INTEGRABLE SYSTEM AND ITS INTEGRABLE COUPLINGS, TWO HIERARCHIES OF NONLINEAR SOLITON EQUATIONS, NEW INTEGRABLE SYMPLECTIC MAP AND DISCRETE INTEGRABLE COUPLINGS, Two pairs of Lie algebras and the integrable couplings as well as the Hamiltonian structure of the Yang hierarchy, A new loop algebra system and its discrete integrable coupling system, A \((2 + 1)\)-dimensional multi-component AKNS integrable hierarchy and its expanding model, Reduced equations of the self-dual Yang-Mills equations and applications, Integrable couplings of the Tu hierarchy and its Hamiltonian structure, A subalgebra of Lie algebra A2 and its associated two types of loop algebras, as well as Hamiltonian structures of integrable hierarchy, Construction and separability of nonlinear soliton integrable couplings, The integrable couplings of the generalized coupled Burgers hierarchy and its Hamiltonian structures, A few subalgebras of the Lie algebra \(A_{3}\) and a direct approach for obtaining integrable couplings, Hamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy, A multi-component matrix loop algebra and the multi-component Kaup-Newell (KN) hierarchy, as well as its integrable coupling system, A multi-component integrable hierarchy and its multi-component expanding integrable model, A simple method for generating integrable hierarchies with multi-potential functions, Super Jaulent-Miodek hierarchy and its super Hamiltonian structure, conservation laws and its self-consistent sources, The multi-component TA hierarchy and its multi-component integrable couplings system with six arbitrary functions, An integrable \(\text{SO}(3,\mathbb{R})\)-counterpart of the Heisenberg soliton hierarchy, Positive and negative hierarchies of nonlinear integrable lattice models and three integrable coupling systems associated with a discrete spectral problem, A new Lax integrable hierarchy, \(N\) Hamiltonian structure and its integrable couplings system, The multi-component KdV hierarchy and its multi-component integrable coupling system, A general method for generating multicomponent integrable hierarchies, A generalized AKNS hierarchy and its bi-Hamiltonian structures, A new algebraic system and its applications, Couplings of a fifth order nonlinear integrable equation: multiple kink solutions, Hamiltonian and super-Hamiltonian extensions related to Broer-Kaup-Kupershmidt system, A super integrable hierarchy and its nonlinear super integrable Hamiltonian couplings, A FAMILY OF NEW DISCRETE EQUATIONS ASSOCIATED WITH LOTKA–VOLTERRA LATTICE AND ITS INTEGRABLE COUPLINGS, A generalized MKdV hierarchy, tri-Hamiltonian structure, higher-order binary constrained flows and its integrable couplings system, A new Lie algebra, a corresponding multi-component integrable hierarchy and an integrable coupling, Bi-integrable couplings associated with \(\mathrm{so}(3,\mathbb{R})\), Some generalized isospectral-nonisospectral integrable hierarchies, A kind of nonisospectral and isospectral integrable couplings and their Hamiltonian systems, THE INTEGRABLE PROPERTY OF LOTKA–VOLTERRA TYPE DISCRETE NONLINEAR LATTICE SOLITON SYSTEMS, Multi-component Gerdjikov-Ivanov system and its Riemann-Hilbert problem under zero boundary conditions, THE ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH INTEGRABLE COUPLINGS, A FOUR-BY-FOUR MATRIX EIGENVALUE PROBLEM, RELATED HIERARCHY OF LAX INTEGRABLE EQUATIONS AND THEIR HAMILTONIAN STRUCTURES, A NEW INTEGRABLE LATTICE HIERARCHY AND ITS TWO DISCRETE INTEGRABLE COUPLINGS, A GENERALIZED LEVI HIERARCHY AND ITS INTEGRABLE COUPLINGS, Multi-component integrable couplings for the Ablowitz-Kaup-Newell-Segur and Volterra hierarchies, THE LIOUVILLE INTEGRABLE LATTICE EQUATIONS ASSOCIATED WITH A DISCRETE THREE-BY-THREE MATRIX SPECTRAL PROBLEM, A NEW METHOD FOR GENERATING A NEW INTEGRABLE SYSTEM, GENERALIZED mKdV EQUATION, LIOUVILLE EQUATION, SINE-GORDON EQUATION AND SINH-GORDON EQUATION AS WELL AS A FORMAL BÄCKLUND TRANSFORMATION, TWO ENLARGED LOOP ALGEBRAS FOR OBTAINING NEW INTEGRABLE HIERARCHIES, A new soliton hierarchy associated with \(\mathrm{so} (3, \mathbb R)\) and its conservation laws, Two integrable couplings of a generalized d-Kaup-Newell hierarchy and their Hamiltonian and bi-Hamiltonian structures, THE NEGATIVE AND POSITIVE INTEGRABLE COUPLING HIERARCHIES DERIVED FROM A FOUR BY FOUR MATRIX SPECTRAL PROBLEM, Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with \(\mathrm{SO}(3)\), A hierarchy of integrable nonlinear lattice equations and its two integrable coupling systems, A SOLITON HIERARCHY FROM THE LEVI SPECTRAL PROBLEM AND ITS TWO INTEGRABLE COUPLINGS, HAMILTONIAN STRUCTURE, A SIMPLE METHOD TO CONSTRUCT INTEGRABLE COUPLING SYSTEM FOR THE MKdV EQUATION HIERARCHY, A HIERARCHY OF DISCRETE INTEGRABLE SYSTEM AND ITS COUPLED ENLARGED INTEGRABLE SYSTEM, Riemann-Hilbert problems and soliton solutions for a multi-component cubic-quintic nonlinear Schrödinger equation, \( \bar\partial \)-dressing method for a few \((2+1)\)-dimensional integrable coupling systems, A new multi-component integrable coupling and its application to isospectral and nonisospectral problems, COUPLING INTEGRABLE COUPLINGS, Characters of explicit solutions for a semidiscrete integrable coupled equation, A NEW SOLITON HIERARCHY AND ITS TWO KINDS OF EXPANDING INTEGRABLE MODELS AS WELL AS HAMILTONIAN STRUCTURE, SUPER-BURGERS SOLITON HIERARCHY AND ITS SUPER-HAMILTONIAN STRUCTURE, TWO (2+1)-DIMENSIONAL INTEGRABLE COUPLINGS OF THE KN HIERARCHY AND CORRESPONDING HAMILTONIAN STRUCTURES, Nonlinear super integrable Hamiltonian couplings, A hierarchy of discrete integrable coupling system with self-consistent sources, ON INTEGRABLE COUPLINGS OF THE DISPERSIVE LONG WAVE HIERARCHY AND THEIR HAMILTONIAN STRUCTURE, A NEW EXPANDING INTEGRABLE HIERARCHY OF KAUP–NEWELL HIERARCHY, An integrable system and associated integrable models as well as Hamiltonian structures, INTEGRABLE COUPLINGS AND NEW EXACT SOLUTIONS FOR THE NONISOSPECTRAL AKNS EQUATION, INTEGRABLE COUPLINGS FOR THE ABLOWITZ–LADIK LATTICE THROUGH ENLARGING ASSOCIATED LAX PAIRS, Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling, Soliton Hierarchies from Matrix Loop Algebras, N-fold Darboux Transformation for Integrable Couplings of AKNS Equations, Trigonal curves and algebro-geometric solutions to soliton hierarchies I, Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System, A direct method for integrable couplings of TD hierarchy, A bi-Hamiltonian formulation for triangular systems by perturbations, Some soliton hierarchies associated with Lie algebras \(\mathfrak{sp}(4)\) and \(\mathfrak{so}(5)\), A novel kind of a multicomponent hierarchy of discrete soliton equations and its application, The relationship between the conservation laws and multi‐Hamiltonian structures of the Kundu equation, Darboux transformations of integrable couplings and applications, An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation, A novel kind of AKNS integrable couplings and their Hamiltonian structures, Integrable Couplings of the Boiti-Pempinelli-Tu Hierarchy and Their Hamiltonian Structures, AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS, KN EQUATIONS HIERARCHY WITH SELF-CONSISTENT SOURCES AND ITS INTEGRABLE COUPLINGS, A BLASZAK–MARCINIAK LATTICE HIERARCHY WITH SELF-CONSISTENT SOURCES, INTEGRABLE COUPLINGS OF SUPER KAUP–NEWELL EQUATION HIERARCHY, A spectral problem based on so$(3,\mathbb {R})$(3,R) and its associated commuting soliton equations, New completely integrable Neumann systems related to the perturbation KdV hierarchy, Two integrable Hamiltonian hierarchies in sl(2,R) and so(3,R) with three potentials, INTEGRABLE HAMILTONIAN HIERARCHIES ASSOCIATED WITH THE EQUATION OF HEAT CONDUCTION, INTEGRABILITY OF A NONAUTONOMOUS COUPLED KdV SYSTEM, Equivalent transformation between the matrices for expanding integrable model of the hierarchy of evolution equation, A FAMILY OF DISCRETE INTEGRABLE COUPLING SYSTEMS AND ITS LIOUVILLE INTEGRABILITY, Two types of new Lie algebras and corresponding hierarchies of evolution equations, An integrable counterpart of the D-AKNS soliton hierarchy from \(\mathrm{so}(3,\mathbb R)\), A three-component Camassa-Holm system with cubic nonlinearity and peakons, Bi-Hamiltonian structure of the extended noncommutative Toda hierarchy, A Multidimensional Superposition Principle: Classical Solitons IV, NEW INTEGRABLE LATTICE HIERARCHY AND ITS INTEGRABLE COUPLING, SPECTRAL RADIUS ANALYSIS OF MATRICES AND THE ASSOCIATED WITH INTEGRABLE SYSTEMS, Bi-integrable couplings and tri-integrable couplings of the modified Ablowitz-Kaup-Newell-Segur hierarchy with self-consistent sources, A super-discrete variational identity and its application for constructing super-discrete Hamiltonian systems, An integrable coupling family of the Toda lattice systems, its bi-Hamiltonian structure, and a related nonisospectral integrable lattice family, Three kinds of coupling integrable couplings of the Korteweg–de Vries hierarchy of evolution equations, Coupling integrable couplings and bi-Hamiltonian structure associated with the Boiti–Pempinelli–Tu hierarchy, A generalized fractional trace identity and Hamiltonian structure of the fractional soliton equation hierarchy, Integrable couplings, bi-integrable couplings and their Hamiltonian structures of the Giachetti-Johnson soliton hierarchy, Integrable nonlocal nonlinear Schrödinger equations associated with 𝑠𝑜(3,ℝ)



Cites Work