共查询到20条相似文献,搜索用时 484 毫秒
1.
Zhang Ping 《Applied mathematics and computation》2010,217(4):1688-1696
In this paper, by using the improved Riccati equations method, we obtain several types of exact traveling wave solutions of breaking soliton equations and Whitham-Broer-Kaup equations. These explicit exact solutions contain solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions. The method employed here can also be applied to solve more nonlinear evolution equations. 相似文献
2.
双函数法及一类非线性发展方程的精确行波解 总被引:5,自引:0,他引:5
给出一种求解非线性发展方程精确行波解的新方法:双函数法。使用此方法,获得了一类非线性发展方程的许多精确行波解,其中包括孤波解和周期解,推广了文献用其它方法取得的结果,同时还获得了许多新的弧波解和周期解,借助于Mathemat-ica,此方法能部分地在计算机上实现。 相似文献
3.
S.A. Khuri 《Chaos, solitons, and fractals》2004,20(5):1037-1040
A complex tanh-function method is introduced for constructing exact travelling wave solutions of nonlinear partial differential equations with complex phases and solutions. The scheme is implemented for obtaining multiple soliton solutions to the nonlinear cubic Schrödinger equation and a generalized Schrödinger-like equation. In additon. an ansätze is proposed to obtain stationary soliton solutions of the cubic Schrödinger equation. 相似文献
4.
?smail Aslan 《Applied mathematics and computation》2009,215(8):3140-3147
We extended the (G′/G)-expansion method to two well-known nonlinear differential-difference equations, the discrete nonlinear Schrödinger equation and the Toda lattice equation, for constructing traveling wave solutions. Discrete soliton and periodic wave solutions with more arbitrary parameters, as well as discrete rational wave solutions, are revealed. It seems that the utilized method can provide highly accurate discrete exact solutions to NDDEs arising in applied mathematical and physical sciences. 相似文献
5.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(8):1967-1973
We modified the so-called extended simplest equation method to obtain discrete traveling wave solutions for nonlinear differential-difference equations. The Wadati lattice equation is chosen to illustrate the method in detail. Further discrete soliton/periodic solutions with more arbitrary parameters, as well as discrete rational solutions, are revealed. We note that using our approach one can also find in principal highly accurate exact discrete solutions for other lattice equations arising in the applied sciences. 相似文献
6.
Ryan Sassaman 《Applied mathematics and computation》2009,215(1):212-220
This paper obtains the 1-soliton solution of five various forms of the generalized nonlinear Klein-Gordon equations. The solitary wave ansatz is used to obtain the soliton solutions of each of these cases. Both topological as well as non-topological soliton solutions are obtained depending on the type of nonlinearity in question. The conserved quantities are also calculated for each of these five forms of generalized nonlinear Klein-Gordon equations. Each of these forms reduce to the previously known results, as special cases. 相似文献
7.
Weiguo Rui 《Communications in Nonlinear Science & Numerical Simulation》2013,18(10):2667-2678
In this paper, by using the integral bifurcation method and the Sakovich’s transformations, we study the two-component short pulse equations of the first kind, different kinds of exact traveling wave solutions with two-loop character, such as two-loop soliton solutions, periodic loop-compacton wave solutions and different kinds of periodic two-loop wave solutions are obtained. Further, we discuss their dynamical behaviors of these exact traveling wave solutions and show their profiles of time evolution by illustrations. This is first time in our research area that we obtain two-soliton solutions of nonlinear partial differential equations under no help of Hirota’s method, inverse scattering method, Darboux transformation and Bächlund transformation. 相似文献
8.
EXACT TRAVELING WAVE SOLUTIONS OF MODIFIED ZAKHAROV EQUATIONS FOR PLASMAS WITH A QUANTUM CORRECTION*
In this article,the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method,hyperbolic seca... 相似文献
9.
Exact travelling wave solutions for nonlinear Schr\"{o}dinger equation with variable coefficients 下载免费PDF全文
Xiuying Liu 《Journal of Applied Analysis & Computation》2017,7(4):1586-1597
In this paper, two nonlinear Schr\"{o}dinger equations with variable coefficients in nonlinear optics are investigated. Based on travelling wave transformation and the extended $(\frac{G''}{G})$-expansion method, exact travelling wave solutions to nonlinear Schr\"{o}dinger equation with time-dependent coefficients are derived successfully, which include bright and dark soliton solutions, triangular function periodic solutions, hyperbolic function solutions and rational function solutions. 相似文献
10.
Filiz Ta?can 《Applied mathematics and computation》2009,215(8):3134-3139
In this paper, we establish exact solutions for (2 + 1)-dimensional nonlinear evolution equations. The sine-cosine method is used to construct exact periodic and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional Boussinesq, breaking soliton and BKP equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems. It is shown that the sine-cosine method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics. 相似文献
11.
Cesar A. Gómez Sierra 《Journal of Computational and Applied Mathematics》2011,235(17):5330-5332
In this work, the improved tanh-coth method is used to obtain wave solutions to a Korteweg-de Vries (KdV) equation with higher-order nonlinearity, from which the standard KdV and the modified Korteweg-de Vries (mKdV) equations with variable coefficients can be derived as particular cases. However, the model studied here include other important equations with applications in several fields of physical and nonlinear sciences. Periodic and soliton solutions are formally derived. 相似文献
12.
In this paper, the integral bifurcation method was used to study the higher order nonlinear wave equations of KdV type (III), which was first proposed by Fokas. Some new travelling wave solutions with singular or nonsingular character are obtained. In particular, we obtain a peculiar exact solution of parametric type in this paper. This one peculiar exact solution has three kinds of wave-form including solitary wave, cusp wave and loop solion under different wave velocity conditions. This phenomenon has proved that the loop soliton solution is one continuous solution, not three breaking solutions though the loop soliton solution “is not in agreement with the Poincaré phase analysis”. 相似文献
13.
Dynamical understanding of loop soliton solution for several nonlinear wave equations 总被引:1,自引:0,他引:1
Ji-bin LI Department of Mathematics Zhejiang Normal University Jinhua China Kunming University of Science Technology Kunming China 《中国科学A辑(英文版)》2007,50(6):773-785
It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution. 相似文献
14.
本文研究了共振长短波方程的孤波解.利用扩展映射法和符号计算,得到许多新的孤波解.这些孤波解能很好地模拟水波,辅助方程用更一般方程代替的扩展映射法能更有效找到这些孤波解.Abstract: In this article,soliton solutions of the long-short wave resonance equations are investigated.By the extended mapping method and symbolic computation,many new exact soliton solutions are obtained.These soliton solutions are fascinating in modeling water waves.The extended mapping method,with the auxiliary ordinary equations replaced by more general ones,is more effective to find these soliton solutions. 相似文献
15.
16.
Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres 总被引:8,自引:0,他引:8
A generalized method, which is called the generally projective Riccati equation method, is presented to find more exact solutions of nonlinear differential equations based upon a coupled Riccati equation. As an application of the method, we choose the higher-order nonlinear Schrodinger equation to illustrate the method. As a result more new exact travelling wave solutions are found which include bright soliton solutions, dark soliton solution, new solitary waves, periodic solutions and rational solutions. The new method can be extended to other nonlinear differential equations in mathematical physics. 相似文献
17.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(9):1748-1757
In this work, we establish exact solutions for coupled nonlinear evolution equations. The extended tanh method is used to construct solitary and soliton solutions of nonlinear evolution equations. The extended tanh method presents a wider applicability for handling nonlinear wave equations. 相似文献
18.
Ahmet Bekir 《Communications in Nonlinear Science & Numerical Simulation》2009,14(4):1038-1042
In this work, we established exact solutions for some nonlinear evolution equations. The extended tanh method was used to construct solitary and soliton solutions of nonlinear evolution equations. The extended tanh method presents a wider applicability for handling nonlinear wave equations. 相似文献
19.
Spatial soliton solutions of a class of generalized nonlinear Schrodinger equations in N-space are discussed analytically and numerically. This achieved using a traveling wavemethod to formulate one-soliton solution and the P-R method is employed to the numerlcal solutions and the interactions between the solirons for the generalized nonlinear systems in Z-pace.The results presented show that the soliton phenomena are characteristics associated with the nonlinearhies of the dynamical systems. 相似文献
20.
YanXu Chi-wangShu 《计算数学(英文版)》2004,22(2):250-274
In this paper, we further develop the local discontinuous Galerkin method to solve three classes of nonlinear wave equations formulated by the general KdV-Burgers type equations, the general fifth-order KdV type equations and the fully nonlinear K(n, n, n) equations, and prove their stability for these general classes of nonlinear equations. The schemes we present extend the previous work of Yan and Shu [30, 31] and of Levy, Shu and Yan [24] on local discontinuous Galerkin method solving partial differential equations with higher spatial derivatives. Numerical examples for nonlinear problems are shown to illustrate the accuracy and capability of the methods. The numerical experiments include stationary solitons, soliton interactions and oscillatory solitary wave solutions.The numerical experiments also include the compacton solutions of a generalized fifthorder KdV equation in which the highest order derivative term is nonlinear and the fully nonlinear K (n, n, n) equations. 相似文献