共查询到20条相似文献,搜索用时 31 毫秒
1.
Darboux transformation with multi-parameters for the
Boussinesq--Burgers (B--B) equation is derived. For an application,
some important explicit solutions of the B--B equation are obtained,
including 2N-soliton solution and periodic solution.
Finally, some elegant and interesting figures are plotted. 相似文献
2.
Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients are studied using the solutions
of Raccati equation. The solitary wave-like solution, the trigonometric periodic wave solution and the rational wave solution
are obtained with a constraint between coefficients. The property of the solutions is numerically investigated. It is shown
that the coefficients of the equation do not change the wave amplitude, but may change the wave velocity.
相似文献
3.
4.
为了构造非线性发展方程的复合型无穷序列精确解, 获得了第二种椭圆方程的Riemann theta 函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bäcklund变换和解的非线性叠加公式, 借助符号计算系统 Mathematica, 以mKdV方程为应用实例, 构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta 函数、Jacobi椭圆函数、双曲函数、 三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解.
关键词:
第二种椭圆方程
Riccati方程
非线性发展方程
Riemann theta 函数无穷序列解 相似文献
5.
6.
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
7.
New multi—soliton solutions and travelling wave solutions of the dispersive long—wave equations 总被引:7,自引:0,他引:7 下载免费PDF全文
Using the extended homogeneous balance method,the (1 1)-dimensional dispersive long-wave equations have been solved.Starting from the homogeneous balance method,we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation.Usually,we can obtain only a type of soliton-like solution.In this paper,we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation. 相似文献
8.
From the point of view of approximate symmetry, the modified
Korteweg--de Vries--Burgers (mKdV--Burgers) equation with weak
dissipation is investigated. The symmetry of a system of the
corresponding partial differential equations which approximate the
perturbed mKdV--Burgers equation is constructed and the
corresponding general approximate symmetry reduction is derived;
thereby infinite series solutions and general formulae can be
obtained. The obtained result shows that the zero-order similarity
solution to the mKdV--Burgers equation satisfies the Painlevé II
equation. Also, at the level of travelling wave reduction, the
general solution formulae are given for any travelling wave solution
of an unperturbed mKdV equation. As an illustrative example, when
the zero-order tanh profile solution is chosen as an initial
approximate solution, physically approximate similarity solutions
are obtained recursively under the appropriate choice of parameters
occurring during computation. 相似文献
9.
In this paper, we studied N-soliton solutions of a new integrable equation studied by Qiao [J. Math. Phys. 48 082701 (2007)]. Firstly, we employed the Darboux matrix method to construct a Darboux transformation for the modified Korteweg-de Vries equation. Then we use the Darboux transformation and a transformation, introduced by Sakovich [J. Math. Phys. 52 023509 (2011)], to derive N-soliton solutions of the new integrable equation from the seed solution. In particular, the multiple soliton solutions are explicitly obtained and shown through some figures. 相似文献
10.
11.
提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统. 相似文献
12.
13.
本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)ut=(g(x)D(u)ux)x+h(x)P(u)ux+q(x)Q(u)进行研究. 当扩散项D(u)取um (m≠-1,0,1)和eu两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解.
关键词:
广义条件对称
精确解
非线性反应扩散方程 相似文献
14.
We find a new family of fifth-order water-wave equations having common invariant manifold of the fourth order. These evolution equations are nonintegrable except for two cases corresponding to the Sawada–Kotera and Kaup–Kupershmidt equations. The invariant manifold of the family is an autonomous equation F-VI from the Cosgrove's classification of fourth-order ODEs having the Painlevé property. Two-parameter solutions of the equation F-VI allow to find two-soliton solutions for this family of evolution equations. 相似文献
15.
16.
Wen-Xiu Ma 《理论物理通讯》2021,73(6):65001
A linear superposition is studied for Wronskian rational solutions to the Kd V equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions. 相似文献
17.
The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes. 相似文献
18.
为了构造高维非线性发展方程的无穷序列类孤子新解, 研究了二阶常系数齐次线性常微分方程, 获得了新结论. 步骤一, 给出一种函数变换把二阶常系数齐次线性常微分方程的求解问题转化为一元二次方 程和Riccati方程的求解问题. 在此基础上, 利用Riccati方程解的非线性叠加公式, 获得了二阶常系数齐次线性常微分方程的无穷序列新解. 步骤二, 利用以上得到的结论与符号计算系统Mathematica, 构造了(2+1)维广义Calogero-Bogoyavlenskii-Schiff (GCBS)方程的无穷序列类孤子新解.
关键词:
常微分方程
非线性叠加公式
高维非线性发展方程
无穷序列类孤子新解 相似文献
19.
In this paper, a new (3+1)-dimensional nonlinear evolution equation is introduced, through the generalized bilinear operators based on prime number p=3. By Maple symbolic calculation, one-, two-lump, and breather-type periodic soliton solutions are obtained, where the condition of positiveness and analyticity of the lump solution are considered. The interaction solutions between the lump and multi-kink soliton, and the interaction between the lump and breather-type periodic soliton are derived, by combining multi-exponential function or trigonometric sine and cosine functions with a quadratic one. In addition, new interaction solutions between a lump, periodic-solitary waves, and one-, two- or even three-kink solitons are constructed by using the ansatz technique. Finally, the characteristics of these various solutions are exhibited and illustrated graphically. 相似文献