Predictability, fast calculation and simulation for the interaction solutions to the cylindrical Kadomtsev-Petviashvili equation

Abstract

The cylindrical Kadomtsev-Petviashvili (cKP) equation related to cylindrical geometry, as one type of the variable-coefficient KP equation, is widely used to describe nonlinear phenomena in fluid, plasma and other fields. With symbolic computation, we have derived the multi-soliton solutions, rational solutions, lump solutions and interaction solutions to the cKP equation based on its bilinear representation. The interaction solutions include two types: The interaction between lump and stripe, and the interaction between lump and soliton. Moreover, we have proposed a new approach to search for the interaction solutions, which can decrease the complexity of the associated nonlinear algebraic equations via reducing the number of the variables. The fast calculation approach provides the condition for the predictability of the interaction solution.