Abstract

A complex modified short pulse (mSP) equation and a nonlocal mSP equation are presented. The integrability and the covariant property of both new equations are shown by constructing their corresponding Lax pair and Darboux transformation, respectively. For the complex mSP equation, some multiple smooth soliton, cuspon soliton, loop soliton, breather and rogue wave solutions are constructed by N-fold Darboux transformation. For the nonlocal mSP equation, some unstable soliton and stable soliton solutions are obtained. The dynamical characteristics of the obtained solutions are shown through some figures.

中文翻译：

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关于两种新型的修正短脉冲方程

摘要

提出了一个复杂的修正短脉冲（mSP）方程和一个非局部mSP方程。通过分别构造它们对应的Lax对和Darboux变换，可以显示两个新方程的可积性和协变特性。对于复杂的mSP方程，通过N折Darboux变换构造了一些多重光滑孤子，cuspon孤子，loop孤子，通气和无赖波解。对于非局部mSP方程，获得了一些不稳定的孤子解和稳定的孤子解。通过一些附图示出了所获得的解决方案的动力学特性。