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81.
A new idea is put forward to modify the Clarkson-Kruskal (CK) direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones. 相似文献
82.
New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 总被引:1,自引:0,他引:1
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In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations. 相似文献
83.
84.
Solving the AKNS Hierarchy by Its Bilinear Form: Generalized Double Wronskian Solutions 总被引:1,自引:0,他引:1
YIN Fu-Mei SUN Ye-Peng CAI Fu-Qing CHEN Deng-Yuan 《理论物理通讯》2008,49(2):401-408
Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed. 相似文献
85.
MA Hong-Cai LOU Sen-Yue 《理论物理通讯》2006,46(6):1005-1010
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches. 相似文献
86.
CAO Li-Ke KE San-Min YUE Rui-Hong 《理论物理通讯》2007,48(4):671-674
A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model. 相似文献
87.
Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation 总被引:1,自引:0,他引:1
LIU Cheng-Shi 《理论物理通讯》2007,48(4):601-604
Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero- Degasperis-Focas equation. 相似文献
88.
Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations 总被引:2,自引:0,他引:2
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This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results. 相似文献
89.
New infinite-dimensional hidden symmetries for the stationary axisymmetric Einstein-Maxwell equations with multiple Abelian gauge fields
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By proposing a so-called extended hyperbolic complex (EHC) function method, an Ernst-like (p+2)×(p+2) matrix EHC potential is introduced for the stationary axisymmetric (SAS) Einstein-Maxwell theory with p Abelian gauge fields (EM-p theory, for short), then the field equations of the SAS EM-p theory are written as a so-called Hauser-Ernst-like self-dual relation for the EHC matrix potential. Two Hauser-Ernst-type EHC linear systems are established, based on which some new parametrized symmetry transformations for the SAS EM-p theory are explicitly constructed. These hidden symmetries are found to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac-Moody algebra su(p+1,1)\otimes R(t,t^{-1}) and Virasoro algebra (without centre charges). All of the SAS EM-p theories for p=0,1,2,… are treated in a unified formulation, p=0 and p=1 correspond, respectively, to the vacuum gravity and the Einstein-Maxwell cases. 相似文献
90.
LIUGuan-Ting FANTian-You 《理论物理通讯》2004,42(4):488-490
Based on a known transform, the exact solutions of (2 1)-dimensional Broer-Kaup equations are investigated by using the method of direct integral. A kind of new exact solutions of Broer Kaup equations are obtained,which contain previous results about solitary wave solutions. 相似文献