Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and m...Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and more new kinds of solitary wave solutions are obtained.展开更多
As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
Different classes of first-principle pseudopotentials are compared and various schemes for pseudopotential generation based on norm conservation are discussed in this paper. BHS (Bachelet, Hamann, and Schlüter)-...Different classes of first-principle pseudopotentials are compared and various schemes for pseudopotential generation based on norm conservation are discussed in this paper. BHS (Bachelet, Hamann, and Schlüter)-scheme and V (Vanderbilt)-modifications are used to derive the KB (Kleinman and Bylander)-pseudopotentials and pseudo wave functions of bismuth. Quality test of pseudopotentials shows that no ghost states occur in the logarithmic der ivatives of pseudo wave functions of Bismuth. The obtained bond length of bismuth dimer with this type of pseudopotentials is in good agreement with previous accurately calculate d ab initio quantum chemical result.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The project supported by National Natural Science Foundation of China under Grant Nos.40045016 and 40175016
文摘Trial function method is applied to solve generalized mKdV (GmKdV for short) equations. It is shownthat GmKdV equations with a real number parameter can be solved directly by this method without a transformation,and more new kinds of solitary wave solutions are obtained.
文摘As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
文摘Different classes of first-principle pseudopotentials are compared and various schemes for pseudopotential generation based on norm conservation are discussed in this paper. BHS (Bachelet, Hamann, and Schlüter)-scheme and V (Vanderbilt)-modifications are used to derive the KB (Kleinman and Bylander)-pseudopotentials and pseudo wave functions of bismuth. Quality test of pseudopotentials shows that no ghost states occur in the logarithmic der ivatives of pseudo wave functions of Bismuth. The obtained bond length of bismuth dimer with this type of pseudopotentials is in good agreement with previous accurately calculate d ab initio quantum chemical result.
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.
