共查询到18条相似文献,搜索用时 78 毫秒
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二维RLW方程和二维SRLW方程的显式精确解 总被引:2,自引:0,他引:2
本文讨论了二维RLW方程和二维SRLW方程孤立波解的性态,通过直接积分的方法求出了这两个方程的显式精确孤立波解,并通过选取初始条件的方法求出了二维RLW方程和二维SRLW方程的另一类精确行波解. 相似文献
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一类广义KdV—Burgers型方程的初边值问题 总被引:3,自引:0,他引:3
本文研究了一类带三阶粘性项的广义KdV-Burgers型方程的初边值问题,运用Galerkin逼近方法,结合能量估计,得到了问题整体解的存在性,正则性,唯一性和稳定性等结果,并在一定条件下讨论了问题的解的渐边行为和“爆破”现象。 相似文献
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Burgers与组合KdV混合型方程的精确解 总被引:20,自引:0,他引:20
张卫国 《数学物理学报(A辑)》1996,16(3):241-248
该文求出了组合KdV方程的渐近值不为零的钟状孤波解和扭状孤波解;求出了Burgers与组合KdV混合型方程ut+auux+bu2ux+ru(xx)+u(xxx)=0的二类扭状孤波解.作为推论,还求出了波方程u(tt)-ku(xx)+pu十qu2+su3=0的钟状和扭状孤波解. 相似文献
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沈惠川 《数学物理学报(A辑)》1996,16(1):40-47
该文将等熵磁流体力学(MHD)或等熵电磁流体力学(EMHD)的基本方程组以及(非相对论的或相对论的)Vlasov方程,分别化为等熵流体力学(HD)表象,建立了上述三类等熵方程之间的对应关系.从而使非相对论Vlasov方程的精确解(它与等熵MHD方程的精确解相对应)和相对论Vlasov方程的精确解(它与等熵EMHD方程的精确解相对应)都可以用(非相对论的和相对论的)等熵HD方程的精确解来表示. 相似文献
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Yingqiu GU 《数学年刊B辑(英文版)》2007,28(5):499-506
In this paper,the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation.This procedure of resolution is based on a canonical form of the metric.According to this procedure,the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution. 相似文献
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RLW-Burgers方程的一类解析解 总被引:1,自引:0,他引:1
谈骏渝 《数学的实践与认识》2001,31(5):545-549
本文给出了 RLW-Burgers方程及 Kd V-Burgers方程的一类解析解 ,且可得到 RLW-Burgers方程的振荡激波解 .这些解可以表示为 Burgers方程和 Kd V方程解的线性组合 ,文末还对文 [8]作了讨论 . 相似文献
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齐次平衡法是把非线性偏微分方程转换成带约束条件的线性偏微分方程的一种很好的方法 .本文在齐次平衡法的基础上具体讨论了KP方程的精确解 ,包括孤波解 ,一般的行波解 ,有理函数解和一种新类型的解 . 相似文献
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Xiaofang Duan Junliang Lu Yaping Ren Rui Ma 《Journal of Nonlinear Modeling and Analysis》2022,4(4):628-649
The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional
propagation of nonlinear dispersive long waves, which has a clear
physical background, and is a more suitable mathematical and
physical equation than the KdV equation. Therefore, the research
on the BBM equation is very important. In this article, we put
forward an effective algorithm, the modified hyperbolic function
expanding method, to build the solutions of the BBM equation. We, by
utilizing the modified hyperbolic function expanding method,
obtain the traveling wave solutions of the BBM equation.
When the parameters are taken as special values, the solitary
waves are also derived from the traveling waves. The traveling
wave solutions are expressed by the hyperbolic functions, the
trigonometric functions and the rational functions. The modified
hyperbolic function expanding method is direct, concise, elementary
and effective, and can be used for many other nonlinear partial
differential equations. 相似文献
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KdV-Burgers方程的对称与孤子解 总被引:1,自引:0,他引:1
考虑KdV-Burgers方程的一些简单对称及其构成的李代数,并利用对称约化方法将KdV-Burgers方程化为常微分方程,从而得到该方程的群不变解.此外,利用多项式展开式的方法去获得KdV-Burgers方程的新的孤子波解. 相似文献
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《分析论及其应用》2017,33(4):323-332
In this paper,we use the complex method to obtain all meromorphic solutions of the complex Zakharov-Kuznetsov modified equal width equation,then find the exact traveling wave solutions of the Zakharov-Kuznetsov modified equal width equation.At last,we give some computer simulations to illustrate our main results. 相似文献
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By means of the classical symmetry method,a hyperbolic Monge-Ampère equation is investigated.The symmetry group is studied and its corresponding group invariant solutions are constructed.Based on the associated vector of the obtained symmetry,the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation,from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully. 相似文献