Residual symmetry, interaction solutions and consistent tanh expansion solvability for the modified Jaulent-Miodek equation

摘要

The residual symmetry for the modified JaulentMiodek equation is obtained with truncated Painlevé expansion method and the form of Lie point symmetry group and the corresponding finite transformations are obtained. Furthermore, the modified Jaulent-Miodek equation also be proved to have consistent tanh expansion form. Based on this property, the interaction solutions between soliton and conoidal periodic wave are explicitly given analytically and graphically in two special cases.