Construction of New Variable Separation Excitations via Extended Projective Ricatti Equation Expansion Method in (2+ 1)- Dimensional Dispersive Long Wave Systems

Abstract

Utilizing the extended projective Ricatti equation expansion method, abundant variable separation solutions of the (2+1)-dimensional dispersive long wave systems are obtained. From the special variable separation solution (38) and by selecting appropriate functions, new types of interaction between the multi-valued and the single-valued solitons, such as semi-foldon and dromion, semi-foldon and peakon, semi-foldon and compacton are found. Meanwhile, we conclude that the solution v is essentially equivalent to the ’universal” formula (1).