Two-component nonlinear waves

TL;DR

This paper derives a generalized model for two-component nonlinear waves, reducing it to coupled nonlinear Schrödinger equations, and presents explicit analytical solutions describing oscillating breathers and vector pulses.

Contribution

It introduces a unified approach to analyze two-component nonlinear waves and provides explicit solutions, extending the understanding of vector solitons in various physical contexts.

Findings

Derived explicit analytical expressions for two-component wave shapes.

Reduced the generalized equation to coupled nonlinear Schrödinger equations.

Identified solutions as oscillating breathers and vector 0π pulses.

Abstract

The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary waves in the different areas of physics. Using both the slowly varying envelope approximation and the generalized perturbation reduction method, the generalized equation is transformed into the coupled nonlinear Schrodinger equations and the two-component nonlinear solitary wave solution is obtained. Explicit analytical expressions for the shape and parameters of two-component nonlinear wave consisting of two breathers oscillating with the sum and difference frequencies and wave numbers are presented. The solution of the generalized equation coincides with the vector 0\pi pulse of the self-induced transparency.