Solitons and infinite dimensional Lie algebras
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Publication:762372
DOI10.2977/prims/1195182017zbMath0557.35091OpenAlexW1983326071MaRDI QIDQ762372
Publication date: 1983
Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2977/prims/1195182017
Infinite-dimensional Lie (super)algebras (17B65) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Partial differential equations of mathematical physics and other areas of application (35Q99)
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Up to five strands in braid, Geodesic distance in planar graphs: an integrable approach, A rigged configuration model for \(B(\infty)\), Duality on Fock spaces and combinatorial energy functions, Enumerative geometry, tau-functions and Heisenberg-Virasoro algebra, SELF-DUAL YANG–MILLS: SYMMETRIES AND MODULI SPACE, Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble, Novel variable separation solutions and exotic localized excitations via the ETM in nonlinear soliton systems, Schlesinger–Bäcklund transformations for the N-component KP, N-solitons, lump solution and interaction phenomenon to the Boussinesq equation, Fibré déterminant et courbes relatives, Higher-order rogue wave solutions of the Sasa–Satsuma equation, BKP tau-functions as square roots of KP tau-functions, Symmetries in the fourth Painlevé equation and Okamoto polynomials, Short wave limit of the Novikov equation and its integrable semi-discretizations, IMMERSION ANOMALY OF DIRAC OPERATOR ON SURFACE IN ℝ3, Soliton resonance and web structure in the Davey–Stewartson system, Eigenvalues of the string constraints for the Kadomtsev-Petviashvili hierarchy, Functional Representation of the AblowitzLadik Hierarchy. II, Darboux Transformation for Drinfel'd–Sokolov–Wilson Equation, Casorati determinant solution for the relativistic Toda lattice equation, Lie symmetries of Hirota’s bilinear equations, Commutative differential operator and a class of solutions for the BKP equation on the singular rational curve, Inverse Spectral Transform for the Modified Kadomtsev-Petviashvili Equation, Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra, Dynamics of lumps and dark–dark solitons in the multi-component long-wave–short-wave resonance interaction system, Self-Consistent Sources Extensions of Modified Differential-Difference KP Equation, Solving the constrained modified KP hierarchy by gauge transformations, Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations, Dispersionless scalar integrable hierarchies, Whitham hierarchy, and the quasiclassical ∂̄-dressing method, The n-component KP hierarchy and representation theory, The fourth Painlevé equation and associated special polynomials, Unnamed Item, Inverse Spectral Transform for the Nonlinear Evolution Equation Generating the Davey-Stewartson and Ishimori Equations, Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable?, Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation, Toda hierarchies and their applications, Linear integral equations, infinite matrices, and soliton hierarchies, Degasperis–Procesi peakon dynamical system and finite Toda lattice of CKP type, Whitham modulation theory for (2 + 1)-dimensional equations of Kadomtsev–Petviashvili type, Highest weight irreducible unitary representations of Lie algebras of infinite matrices. I. The algebra gl(∞), Highest weight irreducible unitarizable representations of Lie algebras of infinite matrices. The algebra A∞, On a zero curvature problem related to the ZS–AKNS operator, New reductions of the Kadomtsev–Petviashvili and two-dimensional Toda lattice hierarchies via symmetry constraints, Localized coherent structures of the Davey–Stewartson equation in the bilinear formalism, Solutions for the vector k-constrained KP hierarchy, Multi-variable reductions of the dispersionless DKP hierarchy, On reductions of the discrete Kadomtsev–Petviashvili-type equations, Soliton structure of the Drinfel’d–Sokolov–Wilson equation, Character expansion of matrix integrals, Infinite-dimensional Lie algebras acting on the solution space of various σ models, A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations, On the infinite-dimensional symmetry group of the Davey–Stewartson equations, Transformation group acting on a self-dual Yang–Mills hierarchy, Derivative and higher-order extensions of Davey–Stewartson equation from matrix Kadomtsev–Petviashvili hierarchy, Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation, Self-consistent-field method and τ-functional method on group manifold in soliton theory. II. Laurent coefficients of soliton solutions for sl̂n and for sûn, Higher-dimensional dromion structures: Jimbo–Miwa–Kadomtsev–Petviashvili system, Solving the constrained KP hierarchy by gauge transformations, Collapse and exponentiation of infinite symmetry algebras of Euclidean projective and Grassmannian σ models, A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equations, Unnamed Item, Unnamed Item, Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev–Petviashvili hierarchy, The discrete potential Boussinesq equation and its multisoliton solutions, General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions, The n -component nonlinear Schrödinger equations: dark–bright mixed N - and high-order solitons and breathers, and dynamics, Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies, On solutions of constrained Kadomtsev–Petviashvili equations: Grammians, A generalized dressing approach for solving the extended KP and the extended mKP hierarchy, Darboux and binary Darboux transformations for the nonautonomous discrete KP equation, Symmetric polynomials, generalized Jacobi-Trudi identities and τ-functions, On moving frames and Toda lattices of BKP and CKP types, Direct linearisation of the discrete-time two-dimensional Toda lattices, Normal Form and Solitons, Hirota’s Bilinear Method and Its Connection with Integrability, A determinant formula for a class of rational solutions of Painlevé V equation, On Gorenstein surfaces dominated by P2, CKP hierarchy and free bosons, On Some Geometric Aspects of Coherent States, Bäcklund transformation of partial differential equations from the Painlevé–Gambier classification. I. Kaup–Kupershmidt equation, Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy, Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies, Lax pairs for integrable lattice systems, Symmetry reductions of the BKP hierarchy, A new extended q-deformed KP hierarchy, Integrability of graph combinatorics via random walks and heaps of dimers, Localized Excitations of a Generalised Jimbo-Miwa Equation, Solutions of the (2 + 1)-Dimensional KP, SK and KK Equations Generated by Gauge Transformations from Nonzero Seeds, ON EQUIVALENCE OF TWO HURWITZ MATRIX MODELS, Multicomponent integrable reductions in the Kadomtsev–Petviashvilli hierarchy, Bilinear form and solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow-water waves, Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters, On Lie algebras of generalized Jacobi matrices, An infinite number of hidden variables in hyper-Kähler metrics, MULTI-SOLITON SOLUTIONS AND THEIR INTERACTIONS FOR THE (2+1)-DIMENSIONAL SAWADA-KOTERA MODEL WITH TRUNCATED PAINLEVÉ EXPANSION, HIROTA BILINEAR METHOD AND SYMBOLIC COMPUTATION, Twisted Quantum Lax Equations, Quantum W1+∞ subalgebras of BCD type and symmetric polynomials, Sato–Bäcklund transformations and string equations of the mKP hierarchy, A Sato formula for reflectionless finite difference operators, KP constraints from reduced multi-component hierarchies, Bilinear expansion of Schur functions in Schur Q-functions: A fermionic approach, AMOEBAS AND INSTANTONS, Commuting flows and conservation laws for noncommutative Lax hierarchies, Bosonic and fermionic representations of endomorphisms of exterior algebras, Modified DKP hierarchy as modified BKP hierarchy, Super modified KP hierarchy in Kac–van de Leur construction, Multiparameter universal characters of B-type and integrable hierarchy, Dynamics of lump solutions, lump-kink solutions and periodic lump solutions in a (3+1)-dimensional generalized Jimbo–Miwa equation, 2D Toda τ functions, weighted Hurwitz numbers and the Cayley graph: Determinant representation and recursion formula, Tau functions, infinite Grassmannians, and lattice recurrences, Unitary matrix integrals, symmetric polynomials, and long-range random walks, Wronskian solutions of the constrained Kadomtsev–Petviashvili hierarchy, Determinant structure of the rational solutions for the Painlevé II equation, The generalized Giambelli formula and polynomial KP and CKP tau-functions, Resonant collisions between lumps and periodic solitons in the Kadomtsev–Petviashvili I equation, Kadomtsev–Petviashvili hierarchy reduction, soliton and semi-rational solutions for the (3+1)-dimensional generalized variable-coefficient shallow water wave equation in a fluid, Universal factorization algebras of polynomials represent Lie algebras of endomorphisms, The ∂̄-dressing method for the (2+1)-dimensional Jimbo-Miwa equation, Integrable semi-discretisation of the Drinfel’d–Sokolov hierarchies, Some new soliton solutions and dynamical behaviours of (3+1)-dimensional Jimbo-Miwa equation, Breathers, interactions between breathers and lumps for a (3 + 1)-dimensional nonlinear evolution equation for the shallow-water waves, Forward scattering for non-linear wave propagation in (3 + 1)-dimensional Jimbo-Miwa equation using singular manifold and group transformation methods, General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation, Bilinear Forms of Integrable Lattices Related to Toda and Lotka-Volterra Lattices, On a Certain Fractional q-Difference and its Eigen Function, Resonant collisions of high-order localized waves in the Maccari system, Connected (n,m)-point functions of diagonal 2-BKP tau-functions and spin double Hurwitz numbers, Quasi-periodic solutions to hierarchies of nonlinear integrable equations and bilinear relations, On the discrete modified KP hierarchies: the Wronskian solutions for their constrained cases, Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras, Diagonal tau-functions of 2d Toda lattice hierarchy, connected \((n,m)\)-point functions, and double Hurwitz numbers, Darboux transformations of the modified BKP hierarchy by fermionic approach, Lump-type and interaction solutions to an extended (3 + 1)-dimensional Jimbo–Miwa equation, On Lax operators, Lagrangian Grassmannians, CKP hierarchy and hyperdeterminantal relations, Integrals of tau functions: a round dance tau function and multimatrix integrals, Interactions among the rogue waves and solitons for a \((2 + 1)\)-dimensional Maccari system in fluid mechanics and nonlinear optics, Multiple soliton solutions and symmetry analysis of a nonlocal coupled KP system, Dynamics of solitons and breathers on a periodic waves background in the nonlocal Mel'nikov equation, M-lump waves and their interactions with multi-soliton solutions for the \((3+1)\)-dimensional Jimbo-Miwa equation, Symmetries and bilinear equations for the modified BKP hierarchy, Flag integrable models and generalized graded algebras, Christoffel transformations for (partial-)skew-orthogonal polynomials and applications, A new generalized constrained modified KP hierarchy, Linear transformations of vertex operators of Hall-Littlewood polynomials, Two types of universal characters and the integrable hierarchies, Multi-Breather, Rogue Wave and Multi-Bright-Dark Soliton Interaction of the (2+1)-Dimensional Nonlocal Fokas System, Algebraic engineering and integrable hierarchies, Instantons in sine-Liouville theory, Tau-function of the B-Toda hierarchy, Multisoliton solutions of the two-component Camassa–Holm system and their reductions, On symmetries of the non-stationary PIIn hierarchy and their applications, Generalized symplectic Schur functions and SUC hierarchy, Elliptic families of solutions to constrained Toda hierarchy, Quantum Gaudin model, spin chains, and universal characters, Novel interaction phenomena of the (3+1)-dimensional Jimbo–Miwa equation, Bilinear expansions of lattices of KP τ -functions in BKP τ -functions: A fermionic approach, A supersymmetric extension of the Toda lattice hierarchy, 2D Yang–Mills Theory and Tau Functions, Nonlinear quantum-dynamical system based on the Kadomtsev-Petviashvili II equation, A supersymmetric extension of the Toda lattice hierarchy, Direct linearization approach to discrete integrable systems associated with ℤ 𝒩 graded Lax pairs, Homology of the Lie algebra gl(\infty, R), A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy, Hirota equations associated with simply laced affine Lie algebras: The cuspidal class E6 of ${\mathfrak {e}}_6^{(1)}$e6(1), Transvectants, modular forms, and the Heisenberg algebra., Multivariate hypergeometric functions as \(\tau\)-functions of Toda lattice and Kadomtsev-Petviashvili equation, Hidden structures of knot invariants, Hidden quantum \(R\)-matrix in the discrete-time classical Heisenberg magnet, On `regular' and `anomalous' solitons of fifth-order equations and an iteration method, Correlators in 2D string theory with vortex condensation, A matrix model for the two-dimensional black hole, Decouple a coupled KdV system of Nutku and O\~guz, Bilinear identities for the constrained modified KP hierarchy, Soliton interaction in the modified Kadomtsev–Petviashvili-(II) equation, The construction of exact solutions of two-dimensional integrable generalizations of Kaup-Kuperschmidt and Sawada-Kotera equations via \(\overline \partial\)-dressing method, Multilinear forms associated with the Yajima-Oikawa system, Solutions of the constrained mKP hierarchy by Boson-Fermion correspondence, The cohomology of the Grassmannian is a gln-module, A Novel Scheme for Nonlinear Evolution Equations Using Symbolic Computations, Cyclotomic quiver Hecke algebras corresponding to minuscule representations, Polynomial tau-functions of BKP and DKP hierarchies, Generalized Wronskian and Grammian Solutions to a Isospectral B-type Kadomtsev-Petviashvili equation, On generalized Lax equations of the Lax triple of the BKP and CKP hierarchies, A modified complex short pulse equation of defocusing type, The gauge transformation of the modified KP hierarchy, Isoperimetric deformations of curves on the Minkowski plane, Functional Representation of the Volterra Hierarchy, The Bethe ansatz in a periodic box–ball system and the ultradiscrete Riemann theta function, Dispersionful analog of the Whitham hierarchy, A new multicomponent CKP hierarchy and solutions, Integrable semi-discretization of a multi-component short pulse equation, Bihamiltonian structure of the two-component Kadomtsev–Petviashvili hierarchy of type B, Self-dual Einstein spaces, heavenly metrics, and twistors, Isotropic Grassmannians, Plücker and Cartan maps, Polynomial tau-functions of the KP, BKP, and the s-component KP hierarchies, LUMP SOLUTIONS TO THE GENERALIZED (2+1)-DIMENSIONAL B-TYPE KADOMTSEV-PETVIASHVILI EQUATION, Quasilinear systems of Jordan block type and the mKP hierarchy, $\mathbb{Z}_\mathcal{N}$ graded discrete integrable systems and Darboux transformations, Exact Solutions to (3+1) Conformable Time Fractional Jimbo–Miwa, Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations, Spatio-Temporal Deformation of Kink-Breather to the (2+1)-Dimensional Potential Boiti–Leon–Manna–Pempinelli Equation, Toda lattice hierarchy and trigonometric Ruijsenaars–Schneider hierarchy, Elliptic solutions to the KP hierarchy and elliptic Calogero–Moser model, Toda lattice hierarchy and soliton equations on square lattice, General higher—order breathers and rogue waves in the two‐component long‐wave–short‐wave resonance interaction model, On a coupled Kadomtsev–Petviashvili system associated with an elliptic curve, Tau‐function formulation for bright, dark soliton and breather solutions to the massive Thirring model, Dynamics of general higher-order rogue waves in the two-component long wave-short wave model of Newell type, Boson–Fermion correspondence of the multi-component constrained mKP hierarchy, Deep learning data-driven multi-soliton dynamics and parameters discovery for the fifth-order Kaup-Kuperschmidt equation, On Lax equations of the two-component BKP hierarchy, General high-order rogue waves in the Hirota equation, The coupled modified Yajima-Oikawa system: model derivation and soliton solutions, Toda lattice with constraint of type B, A new solvable two-matrix model and the BKP tau function, The generalization of strong anisotropic XXZ model and UC hierarchy, General soliton and (semi-)rational solutions of a \((2+1)\)-dimensional sinh-Gordon equation, Rational and semi-rational solutions to the nonlocal Davey-Stewartson III equation, Vector solitons for the (2 + 1)‐dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber, Kac-Schwarz operators of type \(B\), quantum spectral curves, and spin Hurwitz numbers, Polynomial tau-functions of the orthogonal KP, multicomponent orthogonal KP and BUC hierarchies, Unnamed Item
Cites Work
