Non-degenerate Kuznetsov-Ma solitons of Manakov equations and their physical spectra

TL;DR

This paper derives and analyzes a new class of non-degenerate Kuznetsov-Ma solitons within the vector nonlinear Schrödinger (Manakov) equations, revealing their properties, spectra, and formation mechanisms.

Contribution

It introduces the first exact solutions for non-degenerate KMSs in the Manakov system, expanding understanding of vector soliton dynamics.

Findings

Derived exact multi-parameter solutions for non-degenerate KMSs

Presented amplitude profiles and physical spectra of these solutions

Linked non-degenerate KMSs to ordinary vector solitons and numerical excitation methods

Abstract

We study the dynamics of Kuznetsov-Ma solitons (KMS) in the framework of vector nonlinear Schr\"odinger (Manakov) equations. Exact multi-parameter family of solutions for such KMSs is derived. This family of solutions includes the known results as well as the previously unknown solutions in the form of the non-degenerate KMSs. We present the existence diagram of such KMSs that follows from the exact solutions. These non-degenerate KMSs are formed by nonlinear superposition of two fundamental KMSs that have the same propagation period but different eigenvalues. We present the amplitude profiles of new solutions, their exact physical spectra, their link to ordinary vector solitons and offer easy ways of their excitation using numerical simulations.