Year: 2025
Type: article
Abstract: The 2-dimensional Toda lattice (2D Toda) is a completely integrable semi-discrete wave equation with the KP-II equation in its continuous limit. Using Darboux transformations, we prove the linear stability of 1-line solitons for 2D Toda of any size in an exponentially weighted space. We prove that the dominant part of solutions for the linearized equation around a 1-line soliton is a time derivative of the 1-line soliton multiplied by a function of time and transverse variables. The amplitude is described by a 1-dimensional damped wave equation in the transverse variable, as is the case with the linearized KP-II equation.
Author: Tetsu Mizumachi
Institution: Hiroshima University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4415100995