Connections Between Complex PT-Invariant Solutions and Complex Periodic Solutions of Several Nonlinear Equations

TL;DR

This paper explores new links between complex PT-invariant solutions and complex periodic solutions in various nonlinear equations, leading to the discovery of novel solutions.

Contribution

It uncovers novel connections between PT-invariant and periodic solutions, enabling the derivation of new complex solutions for multiple nonlinear equations.

Findings

New complex PT-invariant solutions for several nonlinear equations

Established connections between PT-invariant and periodic solutions

Derived multiple novel solutions using these connections

Abstract

We point out novel connections between complex PT-invariant solutions of several nonlinear equations such as $\phi^4$, $\phi^6$, sine-Gordon, hyperbolic sine-Gordon, double sine-Gordon, double hyperbolic sine-Gordon, mKdV, etc. We then use these connections to obtain several new complex PT-invariant periodic solutions of some of these equations.