Abstract
In this paper, the exact solutions of the (3+1)-dimensional nKdV-nCBS equation are investigated by various approaches. Firstly, according to Lie group theory, the (3+1)-dimensional nKdV-nCBS equation is reduced to two (1+1)-dimensional partial differential equations. Secondly, three different types of exact solutions are obtained by the homoclinic test approach, including the singular kinked-type periodic solitary wave solutions, the kinked solitary wave solutions and the kinked-cross periodic wave solutions. The diagrams of the solutions for the specified parameters are given. Furthermore, taking one reduced equation as an example, the N-soliton solutions are derived. And under some constraints, higher-order soliton solution can degenerate into lower-order soliton solution, which is a specific degeneration phenomenon of this equation.
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