Linear stability of elastic 2-line solitons for the KP-II equation

Mizumachi, Tetsu

doi:10.1090/qam/1676

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Linear stability of elastic $2$-line solitons for the KP-II equation

Author: Tetsu Mizumachi
Journal: Quart. Appl. Math. 82 (2024), 115-226
MSC (2020): Primary 35B35, 37K40; Secondary 35Q35
DOI: https://doi.org/10.1090/qam/1676
Published electronically: July 20, 2023
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Abstract: The KP-II equation was derived by Kadomtsev and Petviashvili to explain stability of line solitary waves of shallow water. Using the Darboux transformations, we study linear stability of $2$-line solitons whose line solitons interact elastically each other. Time evolution of resonant continuous eigenfunctions is described by a damped wave equation in the transverse variable which is supposed to be a linear approximation of the local phase shifts of modulating line solitons.

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