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Burgers equation ut = 2uux + uxx describes a lot of phenomena in physics fields, and it has attracted much attention.In this paper,the Burgers equation is generalized to (2+1) dimensions.By means of the Painlev(e') analysis,the most generalized Painlev(e') integrable(2+1)-dimensional integrable Burgers systems are obtained.Some exact solutions of the generalized Burgers system are obtained via variable separation approach. 相似文献
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求解对流占优Burgers方程的随流格式 总被引:8,自引:0,他引:8
在用差分方法求解对流占优的Burgers方程时,许多常用的差分格式的计算精度会下降。为了提高对流占优问题的计算精度,本文提出非线性对流项的差分格式的设计要求,从而得到对流项的新的差分格式-随流格式。本文通过算例来表明随流格式的优点。 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(4):411-420
We consider the hyperbolic generalization of Burgers equation with polynomial source term. The transformation of auto-Bäcklund type was found. Application of the results is shown in the examples, where kink and bi-kink solutions are obtained from the pair of two stationary ones. 相似文献
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利用扩展齐次平衡法,求出了Burgers方程无穷多个单孤子解和无穷多个有理函数解,特别是得到了Hopf-Cole’s变换和方程初始值问题解的封闭形式.方法简单直接,并且可以推广到其它方程. 相似文献
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Burgers方程的一种并行计算法 总被引:6,自引:1,他引:5
给出了求解Burgers方程的交替分段隐格式,讨论了方法的线性化绝对稳定性,并进行了数值试验.该方法具有并行本性,适合在高性能多处理器的并行计算机上使用. 相似文献
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In this paper, using the direct method of the (2+1)-dimensional multi-component Burgers system, some types of similarity reductions are obtained. The corresponding group explanations of the reductions, Virasoro integrability and soliton solutions of Burgers system are also discussed. 相似文献
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多项式混沌法求解随机Burgers方程 总被引:2,自引:0,他引:2
多项式混沌方法是研究不确定性CFD分析的方法之一。本文介绍了嵌入式多项式混沌方法的数学方法,并以一维Burgers方程为例,介绍了多项式混沌与非线性方程的耦合过程。并采用有限差分法求解一维随机Burgers方程,研究由于黏性系数的不确定性引起的方程解的变化。通过与解析解和采用蒙特卡洛法的模拟结果的对比,对模拟结果进行了验证与确认。研究结果表明多项式混沌方法可以有效地模拟不确定性在流场中的传播,并有很高的速度和精度。 相似文献
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In this article, we study the (2+1)-extension of Burgers equation and the KP equation. At first, based on a known Bäcklund transformation and corresponding Lax pair, an invariance which depends on two arbitrary functions
for (2+1)-extension of Burgers equation is worked out. Given a known solution and using the invariance, we can find solutions of the (2+1)-extension of Burgers equation repeatedly. Secondly, we put forward an invariance of Burgers equation which cannot be directly obtained by constraining the invariance of the (2+1)-extension of Burgers equation. Furthermore, we reveal that the invariance for finding the solutions of Burgers equation can
help us find the solutions of KP equation. At last, based on the
invariance of Burgers equation, the corresponding recursion
formulae for finding solutions of KP equation are digged out. As
the application of our theory, some examples have been put forward in this
article and some solutions of the (2+1)-extension of Burgers
equation, Burgers equation and KP equation are obtained. 相似文献
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从对流速度的物理意义出发,构造出求解Burgers方程的高精度交替分组显式迭代方法,并用线性化方法分析了其稳定性和收敛性,给出模型问题的数值结果。 相似文献
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Burgers equation is reduced into a first-order ordinary differential equation by using travelling wave transformation and it has typical bifurcation characteristics.We can obtain many exact solutions of the Burgers equation,discuss its transcritical bifurcation and control dynamical behaviours by extending the stable region.The transcritical bifurcation exists in the (2 + 1)-dimensional Burgers equation. 相似文献
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为将优化控制技巧用于复杂的地球物理环流模型及其它领域,以Burgers方程为模型,描述了初边值条件的优化控制.在一般化的意义上,给出了连续问题及其相应的离散形式.引入伴随变量,并由此导出伴随方程.比较初始控制中不同频率误差对优化控制的影响,分析了用有限观测数据作空间插值后的数据、方法的优化控制能力及效果,并进行了数值实验. 相似文献
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The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq–Burgers equation 下载免费PDF全文
This paper studies the coupled Burgers equation and the high-order Boussinesq–Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton) solutions and multiple-singular-kink (soliton) solutions are derived for the two equations. 相似文献
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In this paper, the new exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative. We use the first integral method to establish the exact solutions for time-fractional Burgers’ equation, modified Burgers’ equation, and Burgers–Korteweg–de Vries equation. We report that this method is efficient and it can be successfully used to obtain new analytical solutions of nonlinear FDEs. 相似文献
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YANZhen-Ya 《理论物理通讯》2001,36(2):135-138
We obtain Backlund transformation and some new kink-like solitary wave solutions for the generalized Burgers equation in (2 1)-dimensional space,ut 1/2(uδy^-1ux)x-uxx=0,by using the extended homogeneous balance method.As is well known,the introduction of the concept of dromions (the exponentially localized solutions in (2 1)-dimensional space)has triggered renewed interest in (2 1)-dimensional soliton systems.The solutions obtained are used to show that the variable ux admits exponentially localized solutions rather than the physical field u(x,y,t) itself.In addition,it is shown that the equation passes Painleve test. 相似文献
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In this paper, a novel method, named the consistent Burgers equation expansion (CBEE) method, is proposed to solve nonlinear evolution equations (NLEEs) by the celebrated Burgers equation. NLEEs are said to be CBEE solvable if they are satisfied by the CBEE method. In order to verify the effectiveness of the CBEE method, we take (2+1)-dimensional Burgers equation as an example. From the (1+1)-dimensional Burgers equation, many new explicit solutions of the (2+1)-dimensional Burgers equation are derived. The obtained results illustrate that this method can be effectively extended to other NLEEs. 相似文献
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New periodic wave solutions,localized excitations and their interaction for (2+l)-dimensional Burgers equation 下载免费PDF全文
Based on the B/icklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+l)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution). 相似文献
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By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained. 相似文献