2025/05/10 by Tetsu Mizumachi, Mizumachi, Tetsu
Mathematics · Physics and Astronomy · #35B35 #35Q51 #37K40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Primary #Secondary
paper · pdf · doi:10.48550/arxiv.2505.06768
openalex publication_date 2025/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 to 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.