2019/04/21 by Indranil Mukherjee, Mukherjee, Indranil, Partha Guha +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1904.09641
openalex publication_date 2019/04/21 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
The non-holonomic deformations of non-local integrable systems belonging to\nthe Nonlinear Schrodinger family are studied using the Bi-Hamiltonian formalism\nas well as the Lax pair method. The non-local equations are first obtained by\nsymmetry reductions of the variables in the corresponding local systems. The\nbi-Hamiltonian structures of these equations are explicitly derived. The\nbi-Hamiltonian structures are used to obtain the non-holonomic deformation\nfollowing the Kupershmidt ansatz. Further, the same deformation is studied\nusing the Lax pair approach and several properties of the deformation\ndiscussed. The process is carried out for coupled non-local Nonlinear\nSchrodinger and Derivative Nonlinear Schrodinger (Kaup Newell) equations. In\ncase of the former, an exact equivalence between the deformations obtained\nthrough the bi-Hamiltonian and Lax pair formalisms is indicated\n