Lump solutions and interaction solutions for (2+1)-dimensional KPI equation

摘要

The lump solutions and interaction solutions are mainly investigated for the (2 + 1)-dimensional KPI equation. According to relations of the undetermined parameters of the test functions, the N-soliton solutions are showed by computations of the Maple using the Hirota bilinear form for (2 + 1)-dimensional KPI equation. One type of the lump solutions for (2 + 1)-dimensional KPI equation has been deduced by the limit method of the N-soliton solutions. In addition, the interaction solutions between the lump and N-soliton solutions of it are studied by the undetermined interaction functions. The sufficient conditions for the existence of the interaction solutions are obtained. Furthermore, the new breather solutions for the (2 + 1)-dimensional KPI equation are considered by the homoclinic test method via new test functions including more parameters than common test functions.