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The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties. 相似文献
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In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem. 相似文献
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A symmetry-preserving difference scheme for high dimensional nonlinear evolution equations 下载免费PDF全文
In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the original equation and compatibility condition, the difference equations which preserve all Lie point symmetries can be obtained. As an example, invariant difference models of the (2+1)-dimensional Burgers equation are presented. 相似文献
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运用经典李群方法研究了正则长波-KdV方程,得到所有的向量场.然后,将正则长波-KdV方程约化成常微分方程,进一步利用e-φ(ε))展开法和Lambert W函数法求精确解.最后,利用李点对称求正则长波-KdV方程的伴随方程和守恒律. 相似文献
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Residual symmetry,interaction solutions,and conservation laws of the(2+1)-dimensional dispersive long-wave system 下载免费PDF全文
We explore the(2+1)-dimensional dispersive long-wave(DLW) system. From the standard truncated Painlev′e expansion, the B¨acklund transformation(BT) and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the(2+1)-dimensional DLW system is consistent Riccati expansion(CRE) solvable. If the special form of(CRE)-consistent tanh-function expansion(CTE) is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem. 相似文献
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In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given detailed in section 2. This extended method is effective for discreting the high-order (high-dimensional) nonlinear evolution equations. As examples, the invariant difference models of the mKdV equation and the Boussinesq equation are constructed. 相似文献
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In this paper, the Lie group classification method is performed on the fractional partial differential equation(FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations(FODEs) in terms of the Erd′elyi-Kober(E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs. 相似文献
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In this paper,the symmetry group of the(2+1)-dimensional Painlevé integrable Burgers(PIB) equations is studied by means of the classical symmetry method.Ignoring the discussion of the infinite-dimensional subalgebra,we construct an optimal system of one-dimensional group invariant solutions.Furthermore,by using the conservation laws of the reduced equations,we obtain nonlocal symmetries and exact solutions of the PIB equations. 相似文献