Pole Dynamics, Linearization, and Perturbations of the Satsuma--Mimura Equation

2026/06/15 by Yan Lingjuan, Hu Xingbiao, Liu Yajie +1 · 1 voice
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.46298/ocnmp.18568

arxiv published 2026/06/15 · arxiv updated 2026/07/11

Abstract

This paper investigates the pole dynamics and perturbation theory of algebraic soliton solutions associated with the Satsuma--Mimura (SM) equation. First, we give a qualitative analysis of the pole system associated with algebraic soliton solutions, thereby completing a point left open in \citeYan₂025. We then examine three perturbations of the SM equation. The u_x perturbation preserves exact linearizability and leads to an explicit shifted algebraic soliton solution. The u_xx perturbation can be reduced to the unperturbed SM equation by a scaling transformation, which yields the corresponding pole asymptotics and soliton profile. For the genuinely nontrivial Hu_xx perturbation, we derive the first-order perturbation equations and present a short-time numerical simulation based on an explicit Euler discretization. These results clarify how algebraic solitons of the SM equation respond to different perturbative mechanisms.

Citations

• Global Well-Posedness and Soliton Resolution for the Half-Wave Maps Equation with Rational Data
• A direct approach for solving the cubic Szegö equation
• The Calogero--Moser Derivative Nonlinear Schrödinger Equation
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model

Discussions

• Yan Lingjuan, Hu Xingbiao, Liu Yajie, Zhang Yingnan: Pole Dynamics, Linearization, and Perturbations of the Satsuma--Mimura Equation https://arxiv.org/abs/2606.16789 https://arxiv.org/pdf/2606.16789 h [bsky, 0 points, 0 comments]

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