Exact parity and time reversal symmetry invariant and symmetry breaking solutions for a nonlocal KP system

Abstract

A nonlocal Alice-Bob Kadomtsev-Petviashivili (ABKP) system with shifted-parities (${\hat{P}}_s^x$ and ${\hat{P}}_s^y$ parities with shifts for the space variables $x$ and $y$) and delayed time reversal (${\hat{T}}_d$, time reversal with a delay) symmetries is investigated. Some types of ${\hat{P}}_s^y{\hat{P}}_s^x{\hat{T}}_d$ invariant solutions including multiple soliton solutions, Painlevé reductions and soliton and $p$-wave interaction solutions are obtained via ${\hat{P}}_s^y{\hat{P}}_s^x{\hat{T}}_d$ symmetry and the solutions of the usual local KP equation. Some special ${\hat{P}}_s^y{\hat{P}}_s^x{\hat{T}}_d$ symmetry breaking multi-soliton solutions and cnoidal wave solutions are found from the ${\hat{P}}_s^y{\hat{P}}_s^x{\hat{T}}_d$ symmetry reduction of a coupled local KP system.

20 pages