We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as ...We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.展开更多
文摘We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.
