Lump and Stripe Soliton Solutions to the Generalized Nizhnik-Novikov-Veselov Equation**Supported by the National Natural Science Foundation of China under Grant Nos. 11705077 and 11775104, Natural Science Foundation of Zhejiang Province under Grant No. LY14A010005 and Scientific Research Foundation of the First-Class Discipline of Zhejiang Province (B) (No. 201601)

Abstract

With the aid of the truncated Painlevé expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is derived. By combining this quadratic function and an exponential function, the fusion and fission phenomena occur between one lump soliton and a stripe soliton which are two kinds of typical local excitations. Furthermore, by adding a corresponding inverse exponential function to the above function, we can derive the solution with interaction between one lump soliton and a pair of stripe solitons. The dynamical behaviors of such local solutions are depicted by choosing some appropriate parameters.