Transverse linear stability of line solitons for 2D Toda

Tetsu Mizumachi ()
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Tetsu Mizumachi: Hiroshima University

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-31

Abstract: 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.

Keywords: 2D Toda; Line solitary waves; Transverse linear stability; Darboux transformation; Primary 35B35; 37K40; Secondary 35Q51 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00351-0

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