Two-component nonlinear wave of the NLS equation
G. T. Adamashvili
TL;DR
This paper develops a method to derive explicit two-component nonlinear wave solutions for the NLS equation, revealing oscillating components with specific frequency and wave number relations.
Contribution
It introduces a generalized perturbation reduction method to obtain explicit two-component vector nonlinear pulse solutions for the NLS equation.
Findings
Derived explicit analytical expressions for two-component nonlinear pulses.
Showed components oscillate with sum and difference of frequencies and wave numbers.
Provided detailed shape and parameter descriptions of the solutions.
Abstract
Using the generalized perturbation reduction method the scalar nonlinear Schr\"odinger 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 wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.
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Taxonomy
TopicsAdvanced Fiber Laser Technologies · Nonlinear Photonic Systems · Gyrotron and Vacuum Electronics Research