Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method

2026/05/23 by Uyen Le, Alexander Chernyavsky, Barbara Prinari · 1 voice
Mathematics · Physics and Astronomy · #math-ph #math.AP #nlin.SI

paper · pdf · doi:10.1111/sapm.70259

arxiv published 2026/05/23 · arxiv updated 2026/06/09

Abstract

The aim of this paper is to apply Hirota's bilinear method to the integrable discrete Manakov system in the focusing dispersion regime in order to construct and analyze soliton and breather solutions. After deriving the general bilinear form of the system, we show how to obtain fundamental solitons, as well as fundamental and composite breathers. We then obtain solutions exhibiting 2 solitons and 2 breathers and combinations of a soliton and a breather, and discuss all ``two-body'' interactions properties, with particular emphasis on explicit formulas, visualization, and long-time asymptotic behavior, thus rigorously confirming the highly nontrivial interaction properties of these coherent structures.

Citations

• Swinging Waves in the Ablowitz-Ladik Equation
• Breather interactions in the integrable discrete Manakov system and trigonometric Yang-Baxter maps
• On the discrete Kuznetsov-Ma solutions for the defocusing Ablowitz-Ladik equation with large background amplitude
• Modulation instability, periodic anomalous wave recurrence, and blow up in the Ablowitz-Ladik lattices
• Rogue waves arising on the standing periodic waves in the Ablowitz-Ladik equation
• N-Bright-Dark Soliton Solution to a Semi-Discrete Vector Nonlinear Schrödinger Equation
• General rogue waves in the focusing and defocusing Ablowitz-Ladik equations
• Casorati Determinant Form of Dark Soliton Solutions of the Discrete Nonlinear Schrödinger Equation
• Integrable discretization of coupled nonlinear Schrödinger equations
• Integrable semi-discretization of the coupled nonlinear Schrödinger equations
• On Discretizations of the Vector Nonlinear Schrodinger Equation
• Method for Solving the Korteweg-deVries Equation

Discussions

• Uyen Le, Alexander Chernyavsky, Barbara Prinari: Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method https://arxiv.org/abs/2605.24333 https://arxiv [bsky, 0 points, 0 comments]

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