The degeneration of solitary wave solutions and interaction between lump and soliton solutions for the (2+1)-dimensional KdV equation

Abstract The degeneration of solitary wave solutions and interaction solutions between lumps and solitons are primarily explored for the (2+1)-dimensional KdV equation. Firstly, in accordance with the Hirota bilinear form, solitary wave solutions and periodic solitary wave solutions are derived through some new test functions. Then through the parameter limit approach, the lump solutions are gained by degeneration of solitary solutons. Secondly, the interaction solutions between lumps and solitons are given by using of the partial degeneracy of the $N$-soliton solutions. Finally, according to a different test function, some new singular periodic solitary waves solutions are derived via the extended homoclinic test method.