共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, the extended symmetry of generalized variable-coeFficient Kadomtsev-Petviashvili (vcKP) equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of the extended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutions of these veKP equations can be constructed via the simple veKP equations or constant-coefficient KP equations. 相似文献
2.
GE Jian-Ya WANG Rui-Min DAI Chao-Qing ZHANG Jie-Fang 《理论物理通讯》2006,46(4):656-662
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
3.
Variable coefficient nonlinear systems, the Korteweg
de Vries (KdV), the modified KdV (mKdV) and the nonlinear
Schr?dinger (NLS) type equations, are derived from the nonlinear
inviscid barotropic nondivergent vorticity equation in a beta-plane
by means of the multi-scale expansion method in two different ways,
with and without the so-called y-average trick. The
non-auto-B\"acklund transformations are found to transform the
derived variable coefficient equations to the corresponding standard
KdV, mKdV and NLS equations. Thus, many possible exact solutions can
be obtained by taking advantage of the known solutions of these
standard equations. Further, many approximate solutions of the
original model are ready to be yielded which might be applied to
explain some real atmospheric phenomena, such as atmospheric
blocking episodes. 相似文献
4.
Hirota method is used to directly construct quasi-periodic wave solutions for the nonisospectral soliton equation.One and two quasi-periodic wave solutions for the variable-coefficient KdV equation are studied.The well known one-soliton solution can be reduced from the one quasi-periodic wave solution. 相似文献
5.
After considering the variable coefficient of a nonlinear equation as a new dependent variable,some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach.Taking the nonlinear Schrodinger equation as a concrete example,the method is recommended in detail. 相似文献
6.
Consistent Riccati expansion solvability,symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves 下载免费PDF全文
We study a forced variable-coefficient extended Korteweg-de Vries (KdV) equation in fluid dynamics with respect to internal solitary wave. Bäcklund transformations of the forced variable-coefficient extended KdV equation are demonstrated with the help of truncated Painlevé expansion. When the variable coefficients are time-periodic, the wave function evolves periodically over time. Symmetry calculation shows that the forced variable-coefficient extended KdV equation is invariant under the Galilean transformations and the scaling transformations. One-parameter group transformations and one-parameter subgroup invariant solutions are presented. Cnoidal wave solutions and solitary wave solutions of the forced variable-coefficient extended KdV equation are obtained by means of function expansion method. The consistent Riccati expansion (CRE) solvability of the forced variable-coefficient extended KdV equation is proved by means of CRE. Interaction phenomenon between cnoidal waves and solitary waves can be observed. Besides, the interaction waveform changes with the parameters. When the variable parameters are functions of time, the interaction waveform will be not regular and smooth. 相似文献
7.
Describing space and laboratory plasmas, arterial mechanics and
optical fibers, a generalized variable-coefficient nonlinear
Schr?dinger model is hereby under investigation. Four
transformations have been constructed from such a model to the
known standard and cylindrical nonlinear Schr?dinger equations
with the relevant constraints on the variable coefficients
presented. Symbolic computation is performed. Specialities of
those transformations are discussed. Analytic solutions of such a
generalized variable-coefficient model can be obtained via those
transformations from the analytic solutions of the standard and
cylindrical ones. 相似文献
8.
《Waves in Random and Complex Media》2013,23(3):342-349
In this article, we establish exact solutions for variable-coefficient modified KdV equation, variable-coefficient KdV equation, and variable-coefficient diffusion–reaction equations. The modified sine-cosine method is used to construct exact periodic solutions. These solutions may be important for the explanation of some practical physical problems. The obtained results show that the modified sine-cosine method provides a powerful mathematical tool for solving nonlinear equations with variable coefficients. 相似文献
9.
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
10.
In this paper, we first consider
exact solutions for Lienard equation
with nonlinear terms of any order.
Then, explicit exact bell and kink profile solitary-wave solutions
for many nonlinear evolution equations are obtained by means of
results of the Lienard equation and proper deductions, which transform
original partial differential equations into the Lienard one.
These nonlinear equations include compound KdV, compound KdV-Burgers,
generalized Boussinesq, generalized KP and Ginzburg-Landau
equation. Some new solitary-wave solutions are found. 相似文献
11.
In a recent article(Commun. Theor. Phys. 67(2017) 207), three(2+1)-dimensional equations — KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by using different transformation of variables, respectively. In this short note, by adding an adjustment item to original transformation, three more general transformation of variables corresponding to above three equations have been given.Substituting the solutions of the Kd V equation into our transformation of variables, more new exact solutions of the three(2+1)-dimensional equations can be obtained. 相似文献
12.
Based on a new intermediate transformation, a variable-coeFficient hyperbola function method is proposed.Being concise and straightforward, it is applied to the (2 1)-dimensional variable-coeFficient Broer-Kaup system. As a result, several new families of exact soliton-like solutions are obtained, besides the travelling wave. When imposing some conditions on them, the new exact solitary wave solutions of the (2 1)-dimensional Broer Kaup system are given. The method can be applied to other variable-coeFficient nonlinear evolution equations in mathematical physics. 相似文献
13.
14.
Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations 总被引:1,自引:0,他引:1
With the help of some reductions of the self-dual Yang Mills (briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of (2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation, the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new (2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of (2 + 1)-dimensional integrable couplings of a new (2 + 1)- dimensional integrable nonlinear equation. 相似文献
15.
《Physics letters. A》2006,356(1):8-16
The variable-coefficient Korteweg–de Vries (KdV)-typed models, although often hard to be studied, are of current interest in describing various real situations. Under investigation hereby is a large class of the generalized variable-coefficient KdV models with external-force and perturbed/dissipative terms. Recent examples of this class include those in blood vessels and circulatory system, arterial dynamics, trapped Bose–Einstein condensates related to matter waves and nonlinear atom optics, Bose gas of impenetrable bosons with longitudinal confinement, rods of compressible hyperelastic material and semiconductor heterostructures with positonic phenomena. In this Letter, based on symbolic computation, four transformations are proposed from this class either to the cylindrical or standard KdV equation when the respective constraint holds. The constraints have nothing to do with the external-force term. Under those transformations, such analytic solutions as those with the Airy, Hermit and Jacobian elliptic functions can be obtained, including the solitonic profiles. The roles for the perturbed and external-force terms to play are observed and discussed. Investigations on this class can be performed through the properties of solutions of cylindrical and standard KdV equations. 相似文献
16.
17.
《Journal of Nonlinear Mathematical Physics》2013,20(4):458-476
N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are studied by using a generalized version of the dressing method. We first extend the dressing method to the versions with (N + 1) × (N + 1) operators and (2N + 1) × (2N + 1) operators. Then, we obtain three types of N-coupled variable-coefficient equations (N-coupled NLS equations, N-coupled Hirota equations and N-coupled high-order NLS equations). Then, the compatibility conditions are given, which insure that these equations are integrable. Finally, the explicit solutions of the new integrable equations are obtained. 相似文献
18.
In this article,we establish exact solutions for the variable-coefficient Fisher-type equation.The solutions are obtained by the modified sine-cosine method and ansatz method.The soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz method.These solutions are important for the explanation of some practical physical problems.The obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients. 相似文献
19.
In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2N − m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations. 相似文献
20.
Based on a new intermediate transformation, a variable-coefficient hyperbola function method is proposed.Being concise and straightforward, it is applied to the (2 1)-dimensional variable-coefficient Broer Kaup system. As a result, several new families of exact soliton-like solutions are obtained, besides the travelling wave. When imposing some conditions on them, the new exact solitary wave solutions of the (2 1)-dimensional Broer-Kaup system are given. The method can be applied to other variable-coefficient nonlinear evolution equations in mathematical physics. 相似文献