几类非局部非线性方程的新的叠加Kinklike和Pulselike解
Novel Superposed Kinklike and Pulselike Solutions for Several Nonlocal Nonlinear Equations
摘要：
我们证明了一些非局部非线性方程，包括非局部非线性薛定谔（NLS）方程的Ablowitz-Musslimani和Yang变体、非局部修改的Korteweg de Vries（mKdV）方程以及非局部Hirota方程，都存在新颖的扭结状和脉冲状叠加周期解。此外，我们表明，非局部mKdV方程，此外还承认叠加（双曲）扭结-反扭结解决方案。此外，我们表明，而非本地的Ablowitz-Musslimani变种的NLS承认复杂的（宇称时间反转或）PT不变的扭结和脉冲的解决方案，无论是本地NLS也不杨变种的非本地NLS承认这样的解决方案。最后，除了非局部NLS的杨变式外，我们证明了其他三个非局部方程在同一模型中同时存在扭结解和脉冲解。
英文摘要：
We show that a number of nonlocal nonlinear equations including the Ablowitz-Musslimani and the Yang variant of the nonlocal nonlinear Schröd-inger (NLS) equation, nonlocal modified Korteweg de Vries (mKdV) equation as well as the nonlocal Hirota equation admit novel kinklike and pulselike superposed periodic solutions. Further, we show that the nonlocal mKdV equation, in addition also admits the superposed (hyperbolic) kink-antikink solution. Besides, we show that while the nonlocal Ablowitz-Musslimani variant of the NLS admits complex (parity-time reversal or) PT-invariant kink and pulse solutions, neither the local NLS nor the Yang variant of the nonlocal NLS admits such solutions. Finally, except for the Yang variant of the nonlocal NLS, we show that the other three nonlocal equations admit both the kink and pulse solutions in the same model.
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