In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associat...In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.展开更多
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integra...This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.SJ08A05
文摘In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 11505090Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No.BS2015SF009the doctorial foundation of Liaocheng University under Grant No.31805
文摘This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.
