Rogue wave, interaction solutions to the KMM system

TL;DR

This paper applies advanced analytical methods to the KMM system, deriving new exact solutions including rogue waves, breathers, and interaction solutions, enhancing understanding of short wave propagation in ferromagnets.

Contribution

It introduces novel analytic solutions for the KMM system using CTE and Painlevé analysis, including rogue waves and interaction solutions, with solutions for both undamped and damped cases.

Findings

Derived new interaction solutions with arbitrary functions.

Obtained rogue wave solutions and soliton interactions.

First exact solutions for the damped-KMM equation.

Abstract

In this paper, the consistent tanh expansion (CTE) method and the truncated Painlev$\acute{\rm e}$ analysis are applied to the Kraenkel-Manna-Merle (KMM) system, which describes propagation of short wave in ferromagnets. Two series of analytic solutions of the original KMM system (free of damping effect) are obtained via the CTE method. The interaction solutions contain an arbitrary function, which provides a wide variety of choices to acquire new propagation structures. Particularly, the breather soliton, periodic oscillation soliton and multipole instanton are obtained. Furthermore, we obtain some exact solutions of the damped-KMM equation at the first time. On the other hand, a coupled equation containing quadri-linear form and tri-linear form for the original KMM system is obtained by the truncated Painlev$\acute{\rm e}$ analysis, and the rogue wave solution and interaction solutions between rogue wave and multi-soliton for the KMM system are discussed.