Alice-Bob systems, (P)over-cap-(T)over-cap-(C)over-cap symmetry invariant and symmetry breaking soliton solutions

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) over cap), time reversal ((T) over cap), charge conjugation ((C) over cap), and their possible combinations such as (P) over cap(T) over cap,(P) over cap(C) over cap, and (P) over cap(T) over cap(C) over cap, etc., can be successively applied. Especially, some special types of (P) over cap-(T) over cap-(C) over cap group invariant multi-soliton solutions for the KdV-KP-Toda type, mKdV-sG type, and nonlinear Schrodinger equations (NLS) type AB systems are explicitly constructed. The possible (P) over cap(T) over cap symmetry breaking solutions of two special ABKdV systems are explicitly given. Applying the (P) over cap-(T) over cap-(C) over cap symmetries to coupled Ablowitz-Kaup-Newell-Segur systems, some four-place nonlocal NLS systems are also derived. Published by AIP Publishing.