A study of nonholonomic deformations of nonlocal integrable systems belonging to the nonlinear Schrödinger family

I. Mukherjee, P. Guha

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3 Scopus citations

Abstract

The nonholonomic deformations of nonlocal integrable systems belonging to the nonlinear Schrödinger family are studied using the bi-Hamiltonian formalism as well as the Lax pair method. The nonlocal equations are first obtained by symmetry reductions of the variables in the corresponding local systems. The bi-Hamiltonian structures of these equations are explicitly derived. The bi-Hamiltonian structures are used to obtain the nonholonomic deformation following the Kupershmidt ansatz. Further, the same deformation is studied using the Lax pair approach and several properties of the deformation are discussed. The process is carried out for coupled nonlocal nonlinear Schrödinger and derivative nonlinear Schrödinger (Kaup Newell) equations. In the case of the former, an exact equivalence between the deformations obtained through the bi-Hamiltonian and Lax pair formalisms is indicated.

Original languageBritish English
Pages (from-to)293-307
Number of pages15
JournalRussian Journal of Nonlinear Dynamics
Volume15
Issue number3
DOIs
StatePublished - 2019

Keywords

  • Bi-hamiltonian system
  • Kaup – newell equation
  • Lax method
  • Nonholonomic deformation
  • Nonlinear schrödinger equation
  • Nonlocal integrable systems

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