A Study of Nonholonomic Deformations of Nonlocal Integrable Systems Belonging to the Nonlinear Schrödinger Family

DOI10.20537/nd190308zbMath1440.35309arXiv1904.09641OpenAlexW2980727457MaRDI QIDQ5112929

Partha Guha, Indranil Mukherjee

Publication date: 9 June 2020

Published in: Nelineinaya Dinamika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.09641

zbMATH Keywords

nonlinear Schrödinger equationLax methodbi-Hamiltonian systemnonholonomic deformationKaup-Newell equationnonlocal integrable systems

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) Nonholonomic systems related to the dynamics of a system of particles (70F25) Deformations of complex structures (32G05) Nonholonomic dynamical systems (37J60)

Related Items (2)

Non-holonomic and quasi-integrable deformations of the AB equations ⋮ Lagrangian nonlocal nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The concept of quasi-integrability: a concrete example
• KdV6: an integrable system
• A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions
• Quasi-integrability in the modified defocusing non-linear Schrödinger model and dark solitons
• Integrable nonlinear evolution equations on the half-line
• Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
• Complete integrability of nonlocal nonlinear Schrödinger equation
• Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions
• The nonlinear Schrödinger equation on the interval
• Nonholonomic deformation of KdV and mKdV equations and their symmetries, hierarchies and integrability
• Nonholonomic deformation of generalized KdV-type equations
• Integrable Models
• A simple model of the integrable Hamiltonian equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Mechanical systems with nonholonomic constraints
• Study of quasi-integrable and non-holonomic deformation of equations in the NLS and DNLS hierarchy
• Nonlocal nonlinear Schrödinger equations and their soliton solutions
• Integrable Nonlocal Nonlinear Equations
• Integrable systems and reductions of the self-dual Yang–Mills equations
• The Linearization of the Initial-Boundary Value Problem of the Nonlinear Schrödinger Equation
• On the Whitham system for the radial nonlinear Schrödinger equation
• Unified Transform for Boundary Value Problems
• Two-fold integrable hierarchy of nonholonomic deformation of the derivative nonlinear Schrödinger and the Lenells–Fokas equation
• Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method
• The nonlinear Schrödinger equation on the half-line
• PT Symmetry
• On a new non-local formulation of water waves
• Exact accelerating solitons in nonholonomic deformation of the KdV equation with a two-fold integrable hierarchy
• A new integrable generalization of the Korteweg–de Vries equation
• Integrals of nonlinear equations of evolution and solitary waves
• A transform method for linear evolution PDEs on a finite interval

This page was built for publication: A Study of Nonholonomic Deformations of Nonlocal Integrable Systems Belonging to the Nonlinear Schrödinger Family