Novel Superposed Kinklike and Pulselike Solutions for Several Nonlocal Nonlinear Equations

TL;DR

This paper discovers new superposed kinklike and pulselike solutions for various nonlocal nonlinear equations, including nonlocal NLS, mKdV, and Hirota equations, revealing novel PT-invariant solutions and superpositions.

Contribution

The paper introduces novel superposed periodic, kink, and pulse solutions for several nonlocal nonlinear equations, including the nonlocal NLS, mKdV, and Hirota equations, expanding the solution space.

Findings

Nonlocal equations admit novel kinklike and pulselike superposed solutions.

Nonlocal mKdV admits hyperbolic kink-antikink solutions.

PT-invariant solutions exist for the nonlocal Ablowitz-Musslimani NLS.

Abstract

We show that a number of nonlocal nonlinear equations including the Ablowitz-Musslimani and the Yang variant of the nonlocal nonlinear Schr\"od-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.