Elastic collision between one lump wave and multiple stripe waves of nonlinear evolution equations.

A new test function is proposed to construct the elastic one-lump-multi-stripe solutions to the (2+1)-dimensional nonlinear evolution equations via Hirota bilinear forms. The necessary and sufficient conditions for the elastic one-lump-one-stripe solutions, one-lump-two-stripe solutions and one-lump-three-stripe solutions are given to reduce the number of algebraic equations to be solved. The application is made for the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli system in incompressible fluid. Different from the interaction solutions derived by previous test functions, all the collisions between the lump wave and stripe waves are elastic if we ignore the phase shift of the lump wave. The lump wave can pass through the stripe waves. After the collision, the shapes and velocities of the two types of waves remain unchanged. The new test function can be applied to construct elastic one-lump-multi-stripe solutions to other nonlinear evolution equations which cannot be solved by the long wave limit method. The diverse elastic interaction phenomena between one lump wave and stripe waves will be of great significance to discuss the dynamic properties of nonlinear waves. • A new test function is proposed to construct the elastic one-lump-multi-stripe solutions to the (2+1)-dimensional nonlinear evolution equations via Hirota bilinear forms. • The necessary and sufficient conditions for the elastic one-lump-one-stripe solutions, one-lump-two-stripe solutions and one-lump-three-stripe solutions are given to reduce the number of algebraic equations to be solved. • The diverse elastic interaction phenomena between one lump wave and stripe waves will be of great significance to discuss the dynamic properties of nonlinear waves. [ABSTRACT FROM AUTHOR]