New explicit solutions for (2 + 1)-dimensional soliton equation

In this Letter, we study (2 + 1)-dimensional soliton equation by using the bifurcation theory of planar dynamical systems. Following a dynamical system approach, in different parameter regions, we depict phase portraits of a travelling wave system. Bell profile solitary wave solutions, kink profile solitary wave solutions and periodic travelling wave solutions are given. Further, we present the relations between the bounded travelling wave solutions and the energy level h. Through discussing the energy level h, we obtain all explicit formulas of solitary wave solutions and periodic wave solutions.

► (2 + 1)-Dimensional soliton equation reduces to a planar dynamical system.
► The dynamical behavior of the system is studied by analyzing its phase portraits.
► The relations between the travelling wave solutions and the energy level h are presented.
► All explicit solitary wave solutions and periodic wave solutions are obtained.