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1.
Figen Kangalgil 《Physics letters. A》2008,372(11):1831-1835
In this Letter, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. In order to illustrate the validity and the advantages of the method we choose the Ostrovsky equation. As a result, many new and more general exact solutions have been obtained for the equation. 相似文献
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Explicit and exact travelling plane wave solutions of the (2+1)—dimensional Boussinesq equation 总被引:1,自引:0,他引:1 下载免费PDF全文
The deformation mapping method is applied to solve a system of (2+1)-dimensional Boussinesq equations. Many types of explicit and exact travelling plane wave solutions, which contain solitary wave solutions,periodic wave solutions,Jacobian elliptic function solutions and others exact solutions, are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and the cubic nonlinear Klein-Gordon equation. 相似文献
4.
New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation 总被引:2,自引:0,他引:2 下载免费PDF全文
In this paper,
based on hyperbolic tanh-function method and homogeneous balance
method, and auxiliary equation method, some new exact solitary
solutions to the generalized mKdV equation and generalized
Zakharov--Kuzentsov equation are constructed by the method of
auxiliary equation with function transformation with aid of
symbolic computation system Mathematica. The method is of important
significance in seeking new exact solutions to the evolution
equation with arbitrary nonlinear term. 相似文献
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《Physics letters. A》2006,356(2):124-130
A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein–Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham–Broer–Kaup equations. 相似文献
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A new exactly solvable ()-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space–time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation. 相似文献
9.
Hideo Soga 《Communications in Mathematical Physics》1990,133(1):37-52
In the first half of this paper, we construct asymptotic solutions of linear anisotropic elastic equations. In the latter half, we investigate waves reflected by boundaries for plane incident waves in terms of these solutions. Especially, it is examined whether or not the mode-conversion occurs near points where the incident waves hit the boundaries perpendicularly. 相似文献
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用普通Korteweg-de Vries(KdV)方程作变换,构造(3 1)维KdV方程的解,获得了新的孤子解、Jaoobi椭圆函数解、三角函数解和Weierstrass椭圆函数解. 相似文献
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S. I. Denisov W. Horsthemke P. H?nggi 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(4):567-575
We derive the generalized Fokker-Planck equation associated with the
Langevin equation (in the Ito sense) for an overdamped particle in an external
potential driven by multiplicative noise with an arbitrary distribution of the
increments of the noise generating process. We explicitly consider this
equation for various specific types of noises, including Poisson white noise
and Lévy stable noise, and show that it reproduces all Fokker-Planck
equations that are known for these noises. Exact analytical, time-dependent and
stationary solutions of the generalized Fokker-Planck equation are derived and
analyzed in detail for the cases of a linear, a quadratic, and a tailored
potential. 相似文献
13.
The asymptotic behavior of the Cauchy problem for the wave equation with variable velocity and localized initial conditions on the line, semi-axis, and an infinite starlike graph is described. The solution consists of a short-wave and long-wave parts; the shortwave part moves along the characteristics, while the long-wave part satisfies the Goursat or Darboux problem. In the case of a star-like graph, the distribution of energy with respect to the edges is discussed; this distribution depends on the arrangement of the eigensubspaces of the unitary matrix that defines the boundary condition at the vertex of the star. 相似文献
14.
《Physica D: Nonlinear Phenomena》1988,32(2):253-268
We prove the existence of travelling wave solutions to a fifth order partial differential equation, which is a formal asymptotic approximation for water waves with surface tension. These travelling waves are arbitrarily small perturbations of solitary waves, but are not solitary waves themselves, because they approach small amplitude oscillations for large values of the independent variable. This result suggests that for Bond numbers less than one third, there are branches of travelling wave solutions to the water wave equations, which are perturbations of supercritical elevation solitary waves, and which bifurcate from Froude number one and Bond number one third. 相似文献
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Junchao Chen 《Journal of Nonlinear Mathematical Physics》2014,21(3):454-472
In this paper, nonlocal symmetry of the (2+1) dimensional modified generalized long dispersive wave system and its applications are investigated. The nonlocal symmetry related to the eigenfunctions in Lax pairs is derived, and infinitely many nonlocal symmetries are obtained. By introducing three potentials, the prolongation is found to localize the given nonlocal symmetry. Various finite-and infinite-dimensional integrable models are constructed by using the nonlocal symmetry constraint method. Moreover, applying the general Lie symmetry approach to the enlarged system, the finite symmetry transformation and similarity reductions are computed to give novel exact interaction solutions. In particular, the explicit soliton-cnoidal wave solution is obtained for the modified generalized long dispersive wave system, and it can be reduced to the two-dark-soliton solution in one special case. 相似文献
16.
V. G. Bagrov D. M. Gitman V. N. Zadorozhnyi P. M. Lavrov V. N. Shapovalov 《Russian Physics Journal》1980,23(4):276-281
The search for new exact solutions to the Dirac and Klein-Gordon equations initiated in [1] is continued. New solutions are found for axisymmetric fields and one type of nonstationary field of special configuration. The basic notation and system of units of [1] are retained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 10–16, April, 1980. 相似文献
17.
Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method.
It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical
field is still a solution of the equation of interest, except for a phase-shift. The dromion-like structures with elastic
and nonelastic interactions are found. 相似文献
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应用进一步修正的简单方程法对修正的 Benjamin -Bona -Mahoney (mBBM )方程进行求解,给出了mBBM方程新的精确类孤波解,取定某些参数值,便可得到精确孤波解.这种方法也可用于寻找其它常系数以及变系数非线性发展方程(组)的精确解,具有一定的普适性. 相似文献
20.
Y. Matsuno 《Letters in Mathematical Physics》1987,14(4):279-283
New exact classical solutions of the Euclidean Yang-Mills equation are constructed. The exact solutions presented here are characterized by infinite values of topological charges and therefore they are in striking contrast to the well-known instanton and meron solutions which have finite topological charges. 相似文献