Solutions to integrable space-time shifted nonlocal equations. (English) Zbl 1535.35164
Summary: 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 M. J. Ablowitz and Z. H. Musslimani [Phys. Lett., A 409, Article ID 127516, 6 p. (2021; Zbl 07411241)]. Examples include the space-time shifted nonlocal nonlinear Schrödinger and modified Korteweg-de Vries hierarchies and the semi-discrete nonlinear Schrödinger equation. It is shown that these nonlocal integrable equations with or without space-time shift(s) reduction share the same distributions of eigenvalues but the space-time shift(s) brings new constraints to phase terms in solutions.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
Citations:
Zbl 07411241References:
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