Integrable nonlinear Klein-Gordon systems with $\mathcal{P}\mathcal{T}$ nonlocality and/or space-time exchange nonlocality

Abstract

In additional to the parity ($\mathcal{P}$) symmetric, time reversal ($\mathcal{T}$) symmetric, and $\mathcal{P}\mathcal{T}$ symmetric nonlocal integrable systems, some other types of nonlocal integrable Klein-Gordon models with the space-time exchange nonlocality and the moving nolocality are proposed. The Lax pairs of the established nonlinear nonlocal Klein-Gordon equations are explicitly given. A special soliton solution, composed of $\mathcal{P}\mathcal{T}$-symmetric part and $\mathcal{P}\mathcal{T}$-antisymmetric part, is illustrated with the shape change.

References in corpus (2)

• Symmetry breaking of solitons in two-dimensional complex potentials
• Alice-Bob Peakon Systems