Multi-place nonlocal systems

Abstract

Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS) systems and Kadomtsev-Petviashvili (KP) equations are systematically obtained from the discrete symmetry reductions of the coupled local systems. The Lax pairs for the two-place and four-place nonlocal NLS and KP equations are explicitly given. Some types of exact solutions especially the multiple soliton solutions for two-place and four-place KP equations are investigated by means of the group symmetric-antisymmetric separation approach.

26 pages

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• The Fokas-Lenells equations: Bilinear approach
• Solutions to integrable space-time shifted nonlocal equations
• Ren-integrable and ren-symmetric integrable systems
• Integrable nonlinear Klein-Gordon systems with $\mathcal{P}\mathcal{T}$ nonlocality and/or space-time exchange nonlocality
• The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach
• Local and nonlocal complex discrete and semi-discrete sine-Gordon equations and solutions