Indranil Mukherjee
BF 142, BF Block, Sector 1, Bidhannagar, Kolkata, West Bengal, 700064 India
School of Natural and Applied Sciences, Maulana Abul Kalam Azad University of Technology
Publications:
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Mukherjee I., Guha P.
A Study of Nonholonomic Deformations of Nonlocal Integrable Systems Belonging to the Nonlinear Schrödinger Family
2019, Vol. 15, no. 3, pp. 293-307
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.
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