Solitonic interaction of a variable-coefficient (2 + 1)-dimensional generalized breaking soliton equation

In fluids, Korteweg-de Vries-type equations are used to describe certain nonlinear phenomena. Studied in this paper is a variable-coefficient (2 + 1)-dimensional generalized breaking soliton equation, which models the interactions of Riemann waves with long waves. By virtue of the Bell-polynomial approach, bilinear forms of such an equation are obtained. N-soliton solutions are constructed in terms of the exponential functions and Wronskian determinant, respectively. Solitonic propagation and interaction are discussed with the following conclusions: (i) the appearance of characteristic lines such as the periodic and parabolic shapes depends on the form of the variable coefficients; and (ii) interactions of two solitons and three solitons are shown to be elastic.