共查询到20条相似文献,搜索用时 0 毫秒
1.
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
2.
《Physics letters. A》1997,236(4):319-321
New explicit and exact travelling wave solutions to some nonlinear equations are obtained. For some chosen parameters in the nonlinear equations, constants in the explicit solutions are given numerically. 相似文献
3.
Jiefang Zhang 《International Journal of Theoretical Physics》1996,35(8):1793-1798
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations
in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers
equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative Φ4-model equation, the generalized Fisher equation, and the elastic-medium wave equation. 相似文献
4.
This work is devoted to investigating exact solutions of generalized nonlinear fractional diffusion equations with external force and absorption. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we obtain the corresponding exact solution, its diffusive behavior, and the sufficient and necessary conditions for solutions satisfying the boundary condition W(±∞,t)=0 and the sharp initial condition W(x,0)=δ(x). 相似文献
5.
Exact travelling wave solutions to some nonlinear equations of fifth order derivatives are derived by using some accurate ansatz methods. 相似文献
6.
Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in the constructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc. 相似文献
7.
《Physics letters. A》1988,128(9):483-487
A method of constructing travelling wave solutions for nonlinear diffusion equations with polynomial nonlinearities is demonstrated. By certain assumptions some bounded travelling wave solutions are found. One of the results is the first known exact solution for the Fisher equation. 相似文献
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9.
By means of the modified extended tanh-function (METF) method the multiple traveling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. The solutions for the nonlinear equations such as variants of the RLW and variant of the PHI-four equations are exactly obtained and so the efficiency of the method can be demonstrated. 相似文献
10.
In this paper, a two-step ansatz is proposed, which leads to some new solutions to two coupled nonlinear physical equations. 相似文献
11.
12.
R. S. Banerjee 《International Journal of Theoretical Physics》1993,32(5):879-884
We obtain exact solutions of three nonlinear diffusive equations and of the KdV-Burger equation by making an ansatz for the solution in each case. 相似文献
13.
《Physics letters. A》1999,251(1):25-30
In many practical physical problems, the nonlinear wave equations of interest are nonintegrable. In some cases they may be close to an integrable equation, and in this case perturbation techniques are available. However, even in these cases and certainly in general, it is useful to construct exact explicit solutions. Here we introduce a new method for finding exact and explicit periodic travelling wave solutions, from which solitary wave solutions can be extracted if they exist. 相似文献
14.
Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV–mKdV equation are chosen to illustrate the effectiveness of the method. 相似文献
15.
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
16.
17.
Anthony D. Osborne 《Physics letters. A》1981,83(7):311-313
It is shown how to obtain separable solutions, which include travelling-wave solutions as a special case, of a large class of nonlinear wave equations, including the Korteweg-de Vries-Burgers equation and Fisher's equation. 相似文献
18.
V.A. Vladimirov 《Reports on Mathematical Physics》2004,54(2):261-271
A direct algebraic method of obtaining exact solutions to nonlinear PDE's is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some spatially nonlocal hydrodynamic-type model. Special attention is paid to the construction of the kink-like and soliton-like solutions. 相似文献
19.
《Physics letters. A》1998,239(6):359-363
A general semi-analytic method is suggested to obtain the solitary wave solutions for some kinds of nonlinear equations, by the combination of the function-series method and the simulated annealing technique. The validity and reliability of the method are tested by applying it to the study of a generalized φ4 equation. With the proper boundary and initial conditions, pulse-, kink- and breather-like solitons and their combinations are obtained. 相似文献
20.
M. A. Grebenyuk 《Russian Physics Journal》1996,39(10):1001-1006
Exact wave solutions are found for the five-dimensional Einstein equations in a vacuum. The solutions describe the consistent
gravitational scalar wave processes [6] and generalize to five dimensions the known four-dimensional Einstein-Rosen and Bondi-Pirani-Robinson
wave metrics and the Rosen metric. By means of the method of rotations involving the coordinates of x5, the solutions obtained are generalized to the case in which there is an electromagnetic field present. For each of the solutions,
the three-dimensional electric and magnetic field strengths are found.
Moscow University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 112–117, October, 1996. 相似文献