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

TL;DR

This paper explores solutions of a nonlocal KP system that respect or break certain parity and time reversal symmetries, including solitons, Painlevé reductions, and wave interactions, extending local KP solutions.

Contribution

It introduces symmetry-invariant and symmetry-breaking solutions for a nonlocal KP system using shifted parity and delayed time reversal symmetries, linking to local KP solutions.

Findings

Invariant solutions include multi-solitons and Painlevé reductions.

Symmetry-breaking solutions include multi-solitons and cnoidal waves.

New types of solutions are derived from symmetry reductions of local KP equations.

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, Painlev\'e 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.