Rogue waves on an elliptic function background in complex modified Korteweg-de Vries equation

TL;DR

This paper derives rogue wave solutions on elliptic function backgrounds for the complex modified KdV equation using Darboux transformations, revealing how rogue wave amplitudes vary with elliptic modulus.

Contribution

It introduces a novel algebraic method to construct rogue waves on elliptic backgrounds for the complex mKdV equation, analyzing amplitude variations with elliptic modulus.

Findings

Rogue waves are constructed on elliptic function backgrounds using Darboux transformations.

Amplitude of rogue waves decreases with increasing modulus on dn backgrounds.

Amplitude increases with modulus on cn backgrounds.

Abstract

With the assistance of one fold Darboux transformation formula, we derive rogue wave solutions of the complex modified Korteweg-de Vries equation on an elliptic function background. We employ an algebraic method to find the necessary squared eigenfunctions and eigenvalues. To begin we construct the elliptic function background. Then, on top of this background, we create a rogue wave. We demonstrate the outcome for three distinct elliptic modulus values. We find that when we increase the modulus value the amplitude of rogue waves on the dn-periodic background decreases whereas it increases in the case of cn-periodic background.