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Register a new userSolutions to integrable space-time shifted nonlocal equations
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In this paper we present a reduction technique based on bilinearization and double Wronskians (or double Casoratians) to obtain explicit multi-soliton solutions for the integrable space-time shifted nonlocal equations introduced very recently by Ablowitz and Musslimani in [Phys. Lett. A, 2021]. Examples include the space-time shifted nonlocal nonlinear Schrodinger and modified Korteweg-de Vries hierarchies and the semi-discrete nonlinear Schrodinger equation. It is shown that these nonlocal integrable equations with or without space-time shift(s) reduction share same distributions of eigenvalues but the space-time shift(s) brings new constraints to phase terms in solutions.
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In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for infinite class of difference equations. We also provide an example of such a solution that is related to sequence generated by second-order linear recurrent relations.
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Series of deformed Camassa-Holm-type equations are constructed using the Lagrangian deformation and Loop algebra splittings. They are weakly integrable in the sense of modified Lax pairs.
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