In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation...In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrodinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach...In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrodinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.展开更多
The symmetries of a (2+1)-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corre...The symmetries of a (2+1)-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The (1+1) dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.展开更多
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Fu...A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.展开更多
在装备试验与评价(Test and Evaluation,T&E)过程中,设计优选试验与评价方案是确保试验安排的科学合理性、数据分析准确性的前提和基础。对方案的设计,首先,建立了5W1H元模型,从目标、方法、信息、空间、时间、主体等方面对试验与...在装备试验与评价(Test and Evaluation,T&E)过程中,设计优选试验与评价方案是确保试验安排的科学合理性、数据分析准确性的前提和基础。对方案的设计,首先,建立了5W1H元模型,从目标、方法、信息、空间、时间、主体等方面对试验与评价的需求进行了分析;其次,从装备层次、寿命周期、试验环境3个维度对装备全系统的5W1H进行了建模;最后,通过可靠性试验案例阐述了5W1H方法的实施过程。展开更多
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11041003)the Ningbo Natural Science Foundation, China (Grant No. 2009B21003)K.C. Wong Magna Fund in Ningbo University, China
文摘In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrodinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.
基金supported by National Natural Science Foundation of China under Grant Nos.10475055 and 90503006
文摘The symmetries of a (2+1)-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The (1+1) dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.
基金National Natural Science Foundation of China under Grant Nos.90203001,90503006,0475055,and 10647112the Foundation of Donghua University
文摘A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.
文摘在装备试验与评价(Test and Evaluation,T&E)过程中,设计优选试验与评价方案是确保试验安排的科学合理性、数据分析准确性的前提和基础。对方案的设计,首先,建立了5W1H元模型,从目标、方法、信息、空间、时间、主体等方面对试验与评价的需求进行了分析;其次,从装备层次、寿命周期、试验环境3个维度对装备全系统的5W1H进行了建模;最后,通过可靠性试验案例阐述了5W1H方法的实施过程。