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

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.

arXiv comment17 pages, 5 figures and Accepted for Publication in Physica Scripta Journal (2021)

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• Localized Nonlinear Waves on Spatio-Temporally Controllable Backgrounds for a (3+1)-Dimensional Kadomtsev-Petviashvili-Boussinesq Model in Water Waves
• Formation of rogue waves on the periodic background in a fifth-order nonlinear Schrödinger equation