Two-component nonlinear wave of the Hirota equation

TL;DR

This paper derives explicit analytical solutions for two-component nonlinear wave pulses in the Hirota equation, revealing oscillatory behavior with combined frequencies and wave numbers, advancing understanding of complex wave dynamics.

Contribution

It introduces a method to transform the Hirota equation into coupled nonlinear Schrödinger equations and provides explicit solutions for two-component nonlinear pulses.

Findings

Derived explicit analytical expressions for two-component nonlinear pulses.

Showed components oscillate with sum and difference of frequencies and wave numbers.

Enhanced understanding of complex wave interactions in the Hirota equation.

Abstract

Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The components of the pulse oscillate with the sum and difference of the frequencies and the wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.