Ⅰ. INTRODUCTION Early in 1917, Einstein proved that there is a wave solution of gravitational field in vacuum as an approximate solution of weak gravitational field, if these fields satisfy some conditions. This solu...Ⅰ. INTRODUCTION Early in 1917, Einstein proved that there is a wave solution of gravitational field in vacuum as an approximate solution of weak gravitational field, if these fields satisfy some conditions. This solution corresponds to a plane gravitational wave. When the wave propagates along x-axis, the polarized wave will be determined by 2-rank symmetric tensors in yz-plane. So this is a transversal wave. The approximate conditions of weak field展开更多
By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalize...By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalized modified Boussinesq equation. We also discuss the boundedness of these solutions. More over, we study the correlative characteristic of the solitary-wave solutions and the periodic wave solutions along with the travelling wave velocity＇s variation.展开更多
The approximate generalized conditional symmetry （AGCS） approach we previously proposed [Chin. Phys.Lett. 23 （2006） 527] is applied to study the perturbed general KdV-Burgers （KdVB） equation. Complete classifica...The approximate generalized conditional symmetry （AGCS） approach we previously proposed [Chin. Phys.Lett. 23 （2006） 527] is applied to study the perturbed general KdV-Burgers （KdVB） equation. Complete classification of those perturbed general KdVB equations which admit certain types of A GCSs is obtained. Approximate solutions to the perturbed equations can be derived from the corresponding unperturbed ones.展开更多
New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition me...New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.展开更多
文摘Ⅰ. INTRODUCTION Early in 1917, Einstein proved that there is a wave solution of gravitational field in vacuum as an approximate solution of weak gravitational field, if these fields satisfy some conditions. This solution corresponds to a plane gravitational wave. When the wave propagates along x-axis, the polarized wave will be determined by 2-rank symmetric tensors in yz-plane. So this is a transversal wave. The approximate conditions of weak field
基金Supported by the Shanghai Leading Academic Discipline Project(No.T0502)the Science Foundation of the Education Commission of Shanghai(No.07ZZ83).
文摘By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalized modified Boussinesq equation. We also discuss the boundedness of these solutions. More over, we study the correlative characteristic of the solitary-wave solutions and the periodic wave solutions along with the travelling wave velocity＇s variation.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10447007 and 10371098, the China Postdoctoral Science Foundation, the Natural Science Foundation of Shaanxi Province （No 2005A13）, and the Special Research Project of Educational Department of Shaanxi Province （No 03JK060）.
文摘The approximate generalized conditional symmetry （AGCS） approach we previously proposed [Chin. Phys.Lett. 23 （2006） 527] is applied to study the perturbed general KdV-Burgers （KdVB） equation. Complete classification of those perturbed general KdVB equations which admit certain types of A GCSs is obtained. Approximate solutions to the perturbed equations can be derived from the corresponding unperturbed ones.
文摘New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFKdV) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.
