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Transverse linear stability of line solitons for 2D Toda

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  • Tetsu Mizumachi

    (Hiroshima University)

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.

Suggested Citation

  • Tetsu Mizumachi, 2025. "Transverse linear stability of line solitons for 2D Toda," Partial Differential Equations and Applications, Springer, vol. 6(6), pages 1-31, December.
    • Handle: RePEc:spr:pardea:v:6:y:2025:i:6:d:10.1007_s42985-025-00351-0
    DOI: 10.1007/s42985-025-00351-0
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