非局域KP系统的精确宇称、时间反演对称不变量和对称破缺解
Exact parity and time reversal symmetry invariant and symmetry breaking solutions for a nonlocal KP system
摘要：
研究了具有移位宇称（$\hat{P}_s^x$和$\hat{P}_s^y$宇称对空间变量$x$和$y$进行移位）和延迟时间反转（$\hat{T}_d$，延迟时间反转）对称性的非局部Alice-Bob Kadomtsev-Petviashivili（ABKP）系统.利用$\hat{P}_s^y\hat{P}_s^x\hat{T}_d$对称性和通常的局部KP方程的解，得到了一些类型的$\hat{P}_s^y\hat{P}_s^x\hat{T}_d$不变解，包括多重孤子解、Painlevé约化以及孤子与$p$ -波相互作用解.利用耦合局域KP系统的$\hat{P}_s^y\hat{P}_s^x\hat{T}_d$对称约化，得到了一些特殊的$\hat{P}_s^y\hat{P}_s^x\hat{T}_d$对称破缺多孤子解和椭圆余弦波解.
英文摘要：
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.
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