Complete integrability of derivative nonlinear Schrödinger-type equations

Abstract

We study matrix generalizations of derivative nonlinear Schrödinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.

14 pages, LaTeX2e (IOP style), to appear in Inverse Problems

References in corpus (3)

• Integrable semi-discretization of the coupled nonlinear Schrödinger equations
• New integrable systems of derivative nonlinear Schrödinger equations with multiple components
• Complete integrability of derivative nonlinear Schrödinger-type equations

Cited by in corpus (22)

• Integrable discretizations of derivative nonlinear Schroedinger equations
• $H^s$ Bounds for the Derivative Nonlinear Schrödinger Equation
• Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
• Complete integrability of derivative nonlinear Schrödinger-type equations
• Symmetrically coupled higher-order nonlinear Schroedinger equations: singularity analysis and integrability
• On integrable wave interactions and Lax pairs on symmetric spaces
• Systematic method of generating new integrable systems via inverse Miura maps
• On vector analogs of the modified Volterra lattice
• Perturbation theory for nearly integrable multi-component nonlinear PDEs
• New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems
• From AKNS to derivative NLS hierarchies via deformations of associative products
• Algebraic Bethe ansatz for a quantum integrable derivative nonlinear Schrodinger model
• The vector form of Kundu-Eckhaus equation and its simplest solutions
• Bicomplex formulation and Moyal deformation of (2+1)-dimensional Fordy-Kulish systems
• Exact solutions of multicomponent nonlinear Schrödinger equations under general plane-wave boundary conditions
• The algebraic structure behind the derivative nonlinear Schroedinger equation
• Propagation of dark solitons of DNLS equation along a large-scale background
• Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions
• On a new integrable discretization of the derivative nonlinear Schrödinger (Chen-Lee-Liu) equation
• Cole-Hopf Like Transformation for a Class of Coupled Nonlinear Schroedinger Equations
• The Marchenko method to solve the general system of derivative nonlinear Schrödinger equations
• Gauge equivalence among quantum nonlinear many body systems