Kuznetsov-Ma solution and Akhmediev breather for TD equation

2017/07/01 by Junyi Zhu, Linlin Wang, Zhu, Junyi +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1707.00163

openalex publication_date 2017/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the inverse scattering transform for the TD equation, which is related to the Heisenberg spin equation. We note that the TD equation is an integrable model with high nonlinearity, and has singularity at zero. Thus a nonzero boundary condition is introduced in the direct scattering problem. We obtain the N-solitonic solution of the TD equation, and give the Kuznetsov-Ma type solution, rational solution and Akhmediev type breather.

Citations

• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation

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