N-soliton solution and soliton collisions of the (2+1)-dimensional nonlinear long-wave Boussinesq-class equation

Under investigation in this paper is the (2+1)-dimensional nonlinear long-wave Boussinesq-class equation, which models the gravity-capillary waves of finite amplitude on water of finite depth. The bilinear form of this equation is derived by virtue of the generalized binary Bell polynomials. Via symbolic computation, the analytic N-soliton solution is obtained, and the two- and three-soliton solutions are analyzed graphically. Based on those solutions, the properties of (2+1)-dimensional long waves are obtained. Two kinds of elastic collision, i.e. overtaking and head-on, are discussed through the limit expressions of the two-soliton solution. In addition, analysis of the three-soliton solution verifies the conclusions drawn from the two-solition solution.