Alice-Bob systems, P^-T^-Ĉ symmetry invariant and symmetry breaking soliton solutions

Abstract

To describe two-place physical problems, many possible models named Alice-Bob (AB) systems are proposed. To find and to solve these systems, the parity (P^), time reversal (T^), charge conjugation (Ĉ), and their possible combinations such as P^T^, P^Ĉ, and P^T^Ĉ, etc., can be successively applied. Especially, some special types of P^-T^-Ĉ group invariant multi-soliton solutions for the KdV-KP-Toda type, mKdV-sG type, and nonlinear Schrödinger equations (NLS) type AB systems are explicitly constructed. The possible P^T^ symmetry breaking solutions of two special ABKdV systems are explicitly given. Applying the P^-T^-Ĉ symmetries to coupled Ablowitz-Kaup-Newell-Segur systems, some four-place nonlocal NLS systems are also derived.