Multi-solitons of one-dimensional Boussinesq equation

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.

Theorems & Definitions (24)

• Definition 1.1
• proof
• proof
• proof
• proof
• proof
• proof : Proof of Proposition \ref{['Bootstrap3']}
• proof : Proof of Proposition \ref{['UniformEstimates']}
• proof
• proof : Proof of Proposition \ref{['Compactness']}