Soliton Interactions of the “Good” Boussinesq Equation on a Nonzero Background**Supported by the Science Foundation of China University of Petroleum, Beijing under Grant Nos. 2462015YQ0604 and 2462015QZDX02, the Special Funds of the National Natural Science Foundation of China under Grant No. 11247267, and the National Natural Science Foundation of China under Grant Nos. 11371371 and 11401031

Abstract

In this paper, we obtain the soliton solutions for the “good” Boussinesq equation on a constant background. Based on the asymptotic analysis of the solutions, we find that this equation admits both the elastic and resonant soliton interactions, as well as various partially inelastic interactions comprised of such two fundamental interactions. Via picture drawing, we present some examples of soliton interactions on nonzero backgrounds. Our results enrich the knowledge of soliton interactions in the (1+1)-dimensional integrable equation with a single field.