共查询到18条相似文献,搜索用时 62 毫秒
1.
讨论了允许二阶广义条件对称的四阶非线性发展方程.通过广义条件对称方法得到了其对称约化和精确解. 相似文献
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利用广义条件对称,考虑非线性反应扩散方程的精确解,对应于不同的参数讨论,得到相应的方程及其允许的广义条件对称,进而得到方程的精确解. 相似文献
3.
A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. The corresponding reductions and the exact solutions due to the methods of the ordinary differential equations are then given by the methods. The results given here answer partially an open problem proposed by Clarkson, that is how to develop the direct method to seek symmetry reductions of nonlinear PDEs with arbitrary functions. 相似文献
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(2+1)维广义Burgers 方程的Lie点对称, 相似约化和精确解 总被引:2,自引:1,他引:1
讨论了(2+1)维广义Burgers方程.通过Lie群方法求出了该方程的李点对称,并利用李点对称将方程进行相似约化,求出了(2+1)维广义Burgers方程的几种精确解.该方法可以用于研究更高阶的偏微分方程. 相似文献
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1 引言设Ω是R~N(N≥1)上的弧连通的有界区域, Q=Ω×R~+,△为N维Laplace算子,广义多孔介质方程为 在Ω内,(1.1) 在Γ=Ω×R~+(1.2) 在Ω内.(1.3)假设A(u)与f(u)满足: 相似文献
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把内禀对称群分析方法推广应用于(2+2)维非线性微分-差分mToda方程.通过得到的对称,解相应的特征方程,对该方程进行了相似约化.最后通过反变换,构造了几类精确解。 相似文献
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利用直接约化方法得到了(3+1)维Boussinesq方程的对称,约化了方程,并求出其精确解.所得结果推广了已有文献中关于此方程的有关结果. 相似文献
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运用李群对称方法解决Bretherton方程问题,得到方程的对称约化和群不变解,比如幂级数解,最后得出该问题的守恒率. 相似文献
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Michael Kunzinger 《Journal of Mathematical Analysis and Applications》2011,379(1):444-460
We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector fields in involution. Earlier results on the connection between generalized conditional invariance and generalized reduction of evolution equations are revisited. This leads to a no-go theorem on determining equations for operators of generalized conditional symmetry. It is also shown that up to certain equivalences there exists a one-to-one correspondence between generalized conditional symmetries of an evolution equation and parametric families of its solutions. 相似文献
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We introduce the concept of a generalized conditional symmetry. This concept provides an algorithm for constructing physically important exact solutions of non-integrable equations. Examples include 2-shock and 2-soliton solutions. The existence of such exact solutions for non-integrable equations can be traced back to the relation of these equations with integrable ones. In this sense these exact solutions are remnants of integrability.Department of Mathematics and Computer Science and Institute for Nonlinear Studies, Clarkson University, Potsdam, New York 13699-5815. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 263–277, May, 1994. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(4):1631-1641
In this paper, we consider a Kudryashov‐Sinelshchikov equation that describes pressure waves in a mixture of a liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer between liquid and gas bubbles. We show that this equation is rich in conservation laws. These conservation laws have been found by using the direct method of the multipliers. We apply the Lie group method to derive the symmetries of this equation. Then, by using the optimal system of 1‐dimensional subalgebras we reduce the equation to ordinary differential equations. Finally, some exact wave solutions are obtained by applying the simplest equation method. 相似文献
14.
Assuming certain forms of the stream function inverse solutions of an incompressible viscoelastic fluid for a porous medium
channel in the presence of Hall currents are obtained. Expressions for streamlines, velocity components and pressure fields
are described in each case and are compared with the known viscous and second-grade cases. 相似文献
15.
M.S. Bruzón T.M. Garrido E. Recio R. de la Rosa 《Mathematical Methods in the Applied Sciences》2020,43(13):7623-7631
In this work, we consider a Fisher-Kolmogorov equation depending on two exponential functions of the spatial variables. We study this equation from the point of view of symmetry reductions in partial differential equations. Through two-dimensional abelian subalgebras, the equation is reduced to ordinary differential equations. New solutions have been derived and interpreted. 相似文献
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The paper analyzes one of the models of equations of magnetohydrodynamics (MHD) derived earlier. The model was obtained as a result of group classification of the MHD equations in mass Lagrangian coordinates, where all dependent variables in Eulerian coordinates depend on time and two spatial coordinates. The use of Lagrangian coordinates made it possible to solve four equations, which led to the form of reduced equations containing four arbitrary functions: entropy and a three-dimensional vector associated with the magnetic field. The objective of this work is to develop conservation laws and exact solutions for the model. Conservation laws are obtained using Noether's theorem, while exact solutions are obtained either explicitly or by solving a system of ordinary or partial differential equations with two independent variables. Numerical methods are employed for the latter solutions. 相似文献
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Huabing Jia Wei Xu Xiaoshan Zhao Zhanguo Li 《Journal of Mathematical Analysis and Applications》2008,339(2):982-995
This paper considers nonlinear diffusion equations with x-dependent convection and source terms: ut=(Dx(u)ux)+Q(x,u)ux+P(x,u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x. 相似文献
18.
S.M. Myeni 《Journal of Mathematical Analysis and Applications》2009,357(1):225-231
The complete symmetry group of an 1+1 evolution equation of maximal symmetry has been demonstrated to be represented by the six-dimensional Lie algebra of point symmetries sl(2,R)s⊕W, where W is the three-dimensional Heisenberg-Weyl algebra. We construct a complete symmetry group of a 1+2 evolution equation ut=(Fy(u)ux) for some functions F using the point symmetries admitted by the equation. The 1+2 equation is not completely specifiable by point symmetries alone for some specific functions F. We make use of Ansätze already reported by Myeni and Leach [S.M. Myeni, P.G.L. Leach, Nonlocal symmetries and complete symmetry groups of evolution equations, J. Nonlinear Math. Phys. 13 (2006) 377-392] which provide a route to the determination of the required generic nonlocal symmetries necessary to supplement the point symmetries for the complete specification of these 1+2 evolution equations. Further we find that taking some suitable linear combination of Lie point symmetries helps to optimise the procedure of specifying the equation. A general result concerning the number of symmetries required to form a complete symmetry group of evolution is presented in the Conclusion. 相似文献