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arXiv · 2406.17498

Multi-solitons of one-dimensional Boussinesq equation

Vicente Alvarez·Amin Esfahani
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Abstract

The existence of multi-speed solitary waves for the one-dimensional good Boussinesq equation with a power nonlinearity is proven. These solutions are shown to behave at large times as a pair of scalar solitary waves traveling at different speeds. Both subcritical and supercritical cases are treated. The proof is based on the construction of approximations of the multi-speed solitary waves by solving an equivalent system backward in time and using energy methods to obtain uniform estimates.

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Vicente Alvarez, Amin Esfahani. 2024-06-25. Multi-solitons of one-dimensional Boussinesq equation. https://arxiv.org/abs/2406.17498

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