New integrable systems of derivative nonlinear Schrödinger equations with multiple components

DOI10.1016/S0375-9601(99)00272-8zbMath0936.37043arXivsolv-int/9905004MaRDI QIDQ1966871

Miki Wadati, Takayuki Tsuchida

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9905004

zbMATH Keywords

gauge transformationLax pairmatrix form

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (55)

A generalized multi-component Glachette-Johnson (GJ) hierarchy and its integrable coupling system ⋮ Generalized Darboux transformation and rational soliton solutions for Chen-Lee-Liu equation ⋮ Generalized integrable hierarchies of AKNS type, super Dirac type and super NLS-mKdV type ⋮ Riemann-Hilbert approach and long-time asymptotics for the three-component derivative nonlinear Schrödinger equation ⋮ Existence and stability of standing waves for coupled derivative Schrödinger equations ⋮ General rogue wave solutions under SU(2) transformation in the vector Chen-Lee-Liu nonlinear Schrödinger equation ⋮ Numerical methods for the derivative nonlinear Schrödinger equation ⋮ General soliton solutions to a coupled Fokas-Lenells equation ⋮ The Marchenko method to solve the general system of derivative nonlinear Schrödinger equations ⋮ Expansion of Lie Algebra and Its Application ⋮ The Riemann-Hilbert approach for the Chen-Lee-Liu equation with higher-order poles ⋮ Algebro-geometric constructions of semi-discrete Chen-Lee-Liu equations ⋮ Triple Wronskian solutions of the coupled derivative nonlinear Schrödinger equations in optical fibers ⋮ Riemann-Hilbert problem and \(N\)-soliton solutions for the \(n\)-component derivative nonlinear Schrödinger equations ⋮ Optical solitons with Chen-Lee-Liu equation by Lie symmetry ⋮ A complex integrable hierarchy and its Hamiltonian structure for integrable couplings of WKI soliton hierarchy ⋮ A multi-component matrix loop algebra and a unified expression of the multi-component AKNS hierarchy and the multi-component BPT hierarchy ⋮ Existence and construction of compacton solutions ⋮ Two types of generalized integrable decompositions and new solitary-wave solutions for the modified Kadomtsev-Petviashvili equation with symbolic computation ⋮ Gauge equivalence among quantum nonlinear many body systems ⋮ The multi-component dispersive long wave equation hierarchy, its integrable couplings and their Hamiltonian structures ⋮ TWO HIERARCHIES OF NONLINEAR SOLITON EQUATIONS, NEW INTEGRABLE SYMPLECTIC MAP AND DISCRETE INTEGRABLE COUPLINGS ⋮ A new loop algebra and its application to the multi-component S-mKdV hierarchy ⋮ A \((2 + 1)\)-dimensional multi-component AKNS integrable hierarchy and its expanding model ⋮ Derivative non-linear Schrödinger equation: singular manifold method and Lie symmetries ⋮ The multi-component second modified Korteweg-de Vries equation and its two distinct integrable coupling types ⋮ A new multi-component hierarchy and its integrable expanding model ⋮ A matrix Lie superalgebra and its applications ⋮ A generalized multi-component AKNS hierarchy ⋮ The multicomponent generalized Kaup–Newell hierarchy and its multicomponent integrable couplings system with two arbitrary functions ⋮ The multi-component WKI hierarchy ⋮ Periodic solutions of a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kind ⋮ A new loop algebra and its subalgebras ⋮ A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations ⋮ The multi-component KdV hierarchy and its multi-component integrable coupling system ⋮ A general method for generating multicomponent integrable hierarchies ⋮ A new loop algebra and a multi-component integrable system similar to the TC hierarchy ⋮ The multi-component generalized Wadati-Konono-Ichikawa (WKI) hierarchy and its multi-component integrable couplings system with two arbitrary functions ⋮ The multi-component Yang hierarchy and its multi-component integrable coupling system with two arbitrary functions ⋮ The multi-component classical-Boussinesq hierarchy of soliton equations and its multi-component integrable coupling system ⋮ A new Lie algebra, a corresponding multi-component integrable hierarchy and an integrable coupling ⋮ A hierarchy of non-isospectral multi-component AKNS equations and its integrable couplings ⋮ A new loop algebra and its expanded loop algebras, as well as their applications ⋮ Symmetries of Differential Equations and the Problem of Integrability ⋮ A new matrix Lie algebra, the multicomponent Yang hierarchy and its super-integrable coupling system ⋮ Higher-order rogue wave solutions of a general coupled nonlinear Fokas-Lenells system ⋮ New non-isospectral integrable couplings of the AKNS system ⋮ A super hierarchy of coupled derivative nonlinear Schrödinger equations and conservation laws ⋮ Effect of inhomogeneity in energy transfer through alpha helical proteins with interspine coupling ⋮ Integrability aspects and multi-soliton solutions of a new coupled Gerdjikov-Ivanov derivative nonlinear Schrödinger equation ⋮ A generalized Ablowitz–Ladik hierarchy, multi-Hamiltonian structure and Darboux transformation ⋮ Cole-Hopf like transformation for a class of coupled nonlinear Schrödinger equations ⋮ Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation ⋮ Darboux transformation of the second-type derivative nonlinear Schrödinger equation ⋮ The multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear Schrödinger equations and simple Lie algebras
• Generalized Schrödinger equations and Jordan pairs
• Integrable evolution equations on associative algebras
• Jordan algebras and integrable systems
• Vector-matrix generalizations of classical integrable equations
• The Coupled Modified Korteweg-de Vries Equations
• A Class of Exactly Solvable Nonlinear Evolution Equations
• A Generalization of Inverse Scattering Method
• Nonlinear-Evolution Equations of Physical Significance
• Derivative nonlinear Schrodinger equations and Hermitian symmetric spaces
• An exact solution for a derivative nonlinear Schrödinger equation
• Integrable semi-discretization of the coupled nonlinear Schrödinger equations
• Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
• The Two Component Derivative Nonlinear Schrodinger Equation
• Lax Pairs for Four-Wave Interaction Systems
• Derivative Nonlinear Schrödinger Type Equations with Multiple Components and Their Solutions
• Integrable semi-discretization of the coupled modified KdV equations

This page was built for publication: New integrable systems of derivative nonlinear Schrödinger equations with multiple components