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991.
Recently F. Huang [Commun. Theor. Phys. 42 (2004) 903] and X. Tang and P.K. Shukla [Commun. Theor. Phys. 49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing anddissipation on the beta-plane. This equation is governed by two dimensionless parameters, F and β, representing the ratio of the characteristic length scale to the Rossby radius of deformation and the variation of earth' angular rotation, respectively. In the present paper it is shown that in the case F≠ 0 there exists a well-defined point transformation to set β= 0. Theclassification of one- and two-dimensional Lie subalgebras of the Lie symmetry algebra of the potential vorticity equation is given for the parameter combination F≠0 and β = 0. Based upon this classification, distinct classes of group-invariant solutions are obtained and extended to the case β≠ 0. 相似文献
992.
The (3+1)-dimensional Jimbo-Miwa (JM)
equation is solved approximately by using the conformal invariant
asymptotic expansion approach presented by Ruan. By solving the new
(3+1)-dimensional integrable models, which are conformal invariant
and possess Painlevé property, the approximate solutions are
obtained for the JM equation, containing not only one-soliton
solutions but also periodic solutions and multi-soliton solutions.
Some approximate solutions happen to be exact and some approximate
solutions can become exact by choosing relations between the parameters properly. 相似文献
993.
In this paper, we extend the mapping approach to the N-order
Schrödinger equation. In terms of the extended mapping
approach, new families of variable separation solutions with some
arbitrary functions are derived. 相似文献
994.
Recently,a new decomposition of the (2 1)-dimensional Kadomtsev-Petviashvili(KP) equation to a (1 1)-dimensional Broer-Kaup (BK) equation and a (1 1)-dimensional high-order BK equation was presented by Lou and Hu.In our paper,a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems.As application,new explicit soliton-like solutions with five arbitrary parameters for the BK equation,high-order BK equation and KP equation are obtained. 相似文献
995.
An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions. 相似文献
996.
LI Hua-Mei 《理论物理通讯》2003,39(4):395-400
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained. 相似文献
997.
1 AxisymmetryLargeDeformationofCircularMembraneTheproblemofaxisymmetrylargedeformationofcircularmembraneisonewithpracticalsignificance.Hencky (1 91 5) [1]gaveasolutionofpowerseriesundertheuniformforce ;Alekseev (1 951 ) [2 ]gaveananalyticsolutionofcircularmembraneundertheconcentratedforce ,whichisexactonlywhenν=1 3 .ChienWei_zangetal.(1 981 ) [3]gaveananalyticsolutionofthesymmetricalcircularmembraneundertheactionofuniformlydistributedloadsinitscentralportion .Asfortheresultsorotherauthor… 相似文献
998.
Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system 下载免费PDF全文
Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results. 相似文献
999.
王银邦 《应用数学和力学(英文版)》2001,22(1):10-16
IntroductionWhentheboundaryintegralequationmethodisappliedtocrackanalysis,onlynumericalsolutionscanbeobtained ,suchas:thetypicalworksofSnyderandCruse[1],Crouch[2 ],Blandfordetal.[3],Portelaetal.[4 ],Bui[5 ],Weaver[6 ]andWANGetal.[7- 9].Itisverydifficulttoapplytheboundar… 相似文献
1000.
A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results. 相似文献