在普通物理教材中,推导一维平面波的波动方程通常采用两种方法:一是从运动学角度,另一是从动力学角度推出。这两种方法的详细介绍,可参见程守洙、江之永主编《普通物理学》(第三版)§16—3简谐波波动方程。本文试图介绍第三种推导...在普通物理教材中,推导一维平面波的波动方程通常采用两种方法:一是从运动学角度,另一是从动力学角度推出。这两种方法的详细介绍,可参见程守洙、江之永主编《普通物理学》(第三版)§16—3简谐波波动方程。本文试图介绍第三种推导方法。设:在理想的、无吸收的和无限大均匀媒质中,有一行波以波速 u 沿 x 轴传播着。展开更多
A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and im...A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and implicit or explicit based on the parameter choice. The initial value after discretization has second-order accuracy that is consistent with the scheme accuracy. The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm. Experimental results demonstrate the efficiency of the new scheme.展开更多
The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, th...The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.展开更多
Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and giv...Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.展开更多
This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservatio...This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.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.
文摘在普通物理教材中,推导一维平面波的波动方程通常采用两种方法:一是从运动学角度,另一是从动力学角度推出。这两种方法的详细介绍,可参见程守洙、江之永主编《普通物理学》(第三版)§16—3简谐波波动方程。本文试图介绍第三种推导方法。设:在理想的、无吸收的和无限大均匀媒质中,有一行波以波速 u 沿 x 轴传播着。
文摘A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and implicit or explicit based on the parameter choice. The initial value after discretization has second-order accuracy that is consistent with the scheme accuracy. The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm. Experimental results demonstrate the efficiency of the new scheme.
文摘The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx 16
文摘Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029+1 种基金the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001 the Doctoral Foundation of Binzhou University under Grant No.2009Y01
文摘This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.
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.
