Cross-soliton solution, breather soliton, periodic solitary solution, and doubly periodic solution are obtained by using an extended homoclinic test approach with perturbation parameter u 0 and complexity of parameters, respectively. Dynamical feature of cross soliton flow including degeneracy of soliton with different directions, retroflexion of breather soliton for YTSF equation is investigated using the parameter perturbation method. Result shows that the value range of constant equilibrium solution can determine the dynamics of cross soliton for a higher dimensional nonlinear system.
Study on the parameter perturbation behavior about non-traveling wave mechanics to the Zhiber-Shabat equation by Lie symmetry group precise symbolic computation and numerical simulation technology. The Lie point symmetry group and reduced of the equations are obtained. The dynamics simulation model about local excitation parameter perturbation of non-traveling wave soliton are showed by difference scheme and the Matlab numerical calculation of symmetric reduced equation with variable coefficients. The results present the scientific connotation of the new content to the equation and indicate the effectiveness of thought which combined by the symbolic computation and numerical calculation.
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