Discrete Symmetries and Nonlocal Reductions

Abstract

We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.

arXiv comment12 pages

References in corpus (16)

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Cited by in corpus (10)

• The Fokas-Lenells equations: Bilinear approach
• New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential
• Nonlocal KdV Equations
• The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach
• Nonlocal Hydrodynamic Type of Equations
• Local and nonlocal $(2+1)$-dimensional Maccari systems and their soliton solutions
• Multi-component AKNS systems
• Hirota bilinear forms of the AKNS($N$) systems
• $(2+1)$-dimensional AKNS($-N$) Systems: $N=3,4$
• Nonlocal Ernst Equations