We take the （μ^±e^-＋） system as an example, but restrict ourselves to highlight the states with quantum number J^P = 0^-, to explore the different contents of the instantaneous Bethe-Salpeter （BS） equation ...We take the （μ^±e^-＋） system as an example, but restrict ourselves to highlight the states with quantum number J^P = 0^-, to explore the different contents of the instantaneous Bethe-Salpeter （BS） equation and its analog, the relativistic version of Breit equation, by solving them exactly. The results show that the two equations are not equivalent, although they are analogous. Furthermore, since the Breit equation contains extra un-physical solutions, so we point out that it should be abandoned if one wishes to have an accurate description of the bound states for the instantaneous interacting binding systems.展开更多
A new three-component Camassa-Holm equation is introduced. This system is endowed with a structuresimilar to the Camassa-Holm equation. It has peakon solitons and conserves H^1-norm conservation law.
The group classification is carried out on the nonlinear wave equation utt = f（x,u, ux）uzz ＋ g（x,u,uz） by using the preliminary group classification approach. The generators of equivalence group are determined an...The group classification is carried out on the nonlinear wave equation utt = f（x,u, ux）uzz ＋ g（x,u,uz） by using the preliminary group classification approach. The generators of equivalence group are determined and the corresponding reduced forms are obtained. The result of the work is shown in table form.展开更多
In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special c...In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H （x）utt.展开更多
By means of the classical symmetry method,we investigate two types of the(2+1)-dimensional nonlinearKlein-Gorden equation.For the wave equation,we give out its symmetry group analysis in detail.For the secondtype of t...By means of the classical symmetry method,we investigate two types of the(2+1)-dimensional nonlinearKlein-Gorden equation.For the wave equation,we give out its symmetry group analysis in detail.For the secondtype of the(2+1)-dimensional nonlinear Klein-Gorden equation,an optimal system of its one-dimensional subalgebrasis constructed and some corresponding two-dimensional symmetry reductions are obtained.展开更多
文摘We take the （μ^±e^-＋） system as an example, but restrict ourselves to highlight the states with quantum number J^P = 0^-, to explore the different contents of the instantaneous Bethe-Salpeter （BS） equation and its analog, the relativistic version of Breit equation, by solving them exactly. The results show that the two equations are not equivalent, although they are analogous. Furthermore, since the Breit equation contains extra un-physical solutions, so we point out that it should be abandoned if one wishes to have an accurate description of the bound states for the instantaneous interacting binding systems.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10671156 and 10671153
文摘A new three-component Camassa-Holm equation is introduced. This system is endowed with a structuresimilar to the Camassa-Holm equation. It has peakon solitons and conserves H^1-norm conservation law.
基金Supported by NSF-China Grant 10671156NSF of Shaanxi Province of China (SJ08A05) NWU Graduate Innovation and Creativity Funds under Grant No.09YZZ56
文摘The group classification is carried out on the nonlinear wave equation utt = f（x,u, ux）uzz ＋ g（x,u,uz） by using the preliminary group classification approach. The generators of equivalence group are determined and the corresponding reduced forms are obtained. The result of the work is shown in table form.
文摘In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H （x）utt.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030 and 90718041Shanghai Leading Academic Discipline Project under Grant No.B412+1 种基金Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C.Wong Magna Fund in Ningbo University
文摘By means of the classical symmetry method,we investigate two types of the(2+1)-dimensional nonlinearKlein-Gorden equation.For the wave equation,we give out its symmetry group analysis in detail.For the secondtype of the(2+1)-dimensional nonlinear Klein-Gorden equation,an optimal system of its one-dimensional subalgebrasis constructed and some corresponding two-dimensional symmetry reductions are obtained.
