Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions....

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2015-10, Vol.25 (10), p.103114-103114
Main Authors: Kedziora, D J, Ankiewicz, A, Chowdury, A, Akhmediev, N
Format: Article
Language:English
Subjects:
Mathematical analysis
Nonlinear equations
Nonlinear systems
Schrodinger equation
Transformations (mathematics)
Wave functions
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Summary:We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4931710