共查询到19条相似文献,搜索用时 258 毫秒
1.
2.
将行波变换替换为更一般的函数变换,推广了修正的Jacobi椭圆函数展开方法.给出了非线性 Klein-Gordon方程新的周期解.当模m→1或m→0时,这些解退化成相应的孤立波解、三 角函数解和奇异的行波解.对于某些非线性方程,在一定条件下一般变换退化为行波约化.
关键词:
Jacobi椭圆函数
非线性发展方程
精确解 相似文献
3.
基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象.
关键词:
浅水波方程
大尺度正压大气
解析解
非线性波 相似文献
4.
利用改进的G’/G展开方法,借助于计算机代数系统Mathematica成功获得了一大类非线性波动方程一系列新的含有多个参数的精确行波解.这些解包括孤立波解、双曲函数解、三角函数解. 相似文献
5.
提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式,再利用三阶多项式的完 全判别系统求解,由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解
关键词:
试探方程法
非线性发展方程
孤波解
Jacobi椭圆函数
周期解 相似文献
6.
通过把十二个Jacobi椭圆函数分类成四组,提出了新的广泛的Jacobi椭圆函数展开法,利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时,这些解退化为相应的三角函数解或孤立波解和冲击波解.
关键词:
非线性发展方程
Jacobi椭圆函数
双周期解
行波解 相似文献
7.
8.
利用动力系统方法研究一维Tonks-Girardeau原子气区域中Gross-Pitaevskii (GP)方程简化模型的一些精确行波解以及这些精确行波解的动力学行为, 研究系统的参数对行波解的动力学行为的影响. 在不同的参数条件下, 获得了一维Tonks-Girardeau原子气区域中GP方程简化模型的六个行波解的精确参数表达式.
关键词:
动力系统方法
孤立波解
周期波解
扭波解 相似文献
9.
10.
11.
In this paper, we analyze the relation between the shape of the
bounded traveling wave solutions and dissipation coefficient of
nonlinear wave equation with cubic term by the theory and method of
planar dynamical systems. Two critical values which can characterize
the scale of dissipation effect are obtained. If dissipation effect
is not less than a certain critical value, the traveling wave
solutions appear as kink profile; while if it is less than this
critical value, they appear as damped oscillatory. All expressions
of bounded traveling wave solutions are presented, including exact
expressions of bell and kink profile solitary wave solutions, as
well as approximate expressions of damped oscillatory solutions. For
approximate damped oscillatory solution, using homogenization
principle, we give its error estimate by establishing the integral
equation which reflects the relations between the exact and
approximate solutions. It can be seen that the error is an
infinitesimal decreasing in the exponential form. 相似文献
12.
With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Schrödinger equation (GDNLSE) have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given. 相似文献
13.
Cheng-Shi Liu 《Foundations of Physics》2011,41(5):793-804
To find exact traveling wave solutions to nonlinear evolution equations, we propose a method combining symmetry properties
with trial polynomial solution to nonlinear ordinary differential equations. By the method, we obtain some exact traveling
wave solutions to the Burgers-KdV equations and a kind of reaction-diffusion equations with high order nonlinear terms. As
a result, we prove that the Burgers-KdV equation does not have the real solution in the form a
0+a
1tan ξ+a
2tan 2
ξ, which indicates that some types of the solutions to the Burgers-KdV equation are very limited, that is, there exists no
new solution to the Burgers-KdV equation if the degree of the corresponding polynomial increases. For the second equation,
we obtain some new solutions. In particular, some interesting structures in those solutions maybe imply some physical meanings.
Finally, we discuss some classifications of the reaction-diffusion equations which can be solved by trial equation method. 相似文献
14.
In this paper, exact traveling wave solutions of the conformable differential equations have been examined. By means of the wave transformation and properties of the conformable derivative (CD), conformable nonlinear Schrödinger equation (CNLSE) has been converted into an integer order differential equation. To extract optical solutions, the wave profile has been divided into amplitude and phase components. A new extension of the Bäcklund method has been offered and applied to the CNLSE which has important applications in quantum mechanics. Some novel exact traveling wave solutions to the CNLSE with group velocity dispersion and second order spatiotemporal dispersion coefficients are successfully obtained by means of this method. 相似文献
15.
《Waves in Random and Complex Media》2013,23(4):644-655
Mathematical modeling of many autonomous physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear evolution equations plays a significant role in the study of nonlinear physical phenomena. In this article, the enhanced (G′/G)-expansion method has been applied for finding the exact traveling wave solutions of longitudinal wave motion equation in a nonlinear magneto-electro-elastic circular rod. Each of the obtained solutions contains an explicit function of the variables in the considered equations. It has been shown that the applied method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering fields. 相似文献
16.
The solutions to a linear wave equation can satisfy the principle of superposition,i.e.,the linear superposition of two or more known solutions is still a solution of the linear wave equation.We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic,triangle,and exponential functions,and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics.The linear superposition solutions to the generalized KdV equation K(2,2,1),the Oliver water wave equation,and the k(n,n) equation are given.The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed,and the reason why the solutions with the forms of hyperbolic,triangle,and exponential functions can form the linear superposition solutions is also discussed. 相似文献
17.
S. M. Rayhanul Islam Kamruzzaman Khan K. M. Abdul Al Woadud 《Waves in Random and Complex Media》2018,28(2):300-309
The enhanced (G′/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney–Luke equation by using the enhanced (G′/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper. 相似文献
18.
A New Approach to Solve Nonlinear Wave Equations 总被引:3,自引:0,他引:3
From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions. 相似文献
19.
柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象. 相似文献