共查询到20条相似文献,搜索用时 15 毫秒
1.
Khadijo Rashid Adem Chaudry Masood Khalique 《Nonlinear Analysis: Real World Applications》2012,13(4):1692-1702
This paper obtains solutions to the Zakharov-Kuznetsov modified equal width equation with power law nonlinearity. The Lie symmetry approach and the simplest equation method are used to obtain these solutions. Moreover, conservation laws are derived for the underlying equation by employing two approaches: the new conservation theorem and the multiplier method. 相似文献
2.
Pavel N. Ryabov 《Applied mathematics and computation》2010,217(7):3585-3590
The Kudryashov-Sinelshchikov equation for describing the pressure waves in liquid with gas bubbles is studied. New exact solutions of this equation are found. Modification of truncated expansion method is used for obtaining exact solution of this equation. 相似文献
3.
B. van't Hof J. H. M. ten Thije Boonkkamp R. M. M. Mattheij 《Numerical Methods for Partial Differential Equations》1998,14(5):607-625
A finite volume method for the convection-diffusion-reaction equation is presented, which is a model equation in combustion theory. This method is combined with an exponential scheme for the computation of the fluxes. We prove that the numerical fluxes are second-order accurate, uniformly in the local Peclet numbers. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 607–625, 1998 相似文献
4.
Aly R. Seadawy 《Applied Mathematics Letters》2012,25(4):687-691
In the present study, we converted the resulting nonlinear equation for the evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background with self-focusing in a two-dimensional nonlinear Schrödinger (NLS) equation. Applying the function transformation method, the NLS equation was transformed to an ordinary differential equation, which depended only on one function ξ and can be solved. The general solution of the latter equation in ζ leads to a general solution of NLS equation. A new set of exact solutions for the two-dimensional NLS equation is obtained. 相似文献
5.
Nikolay A. Kudryashov Pavel N. Ryabov Dmitry I. Sinelshchikov 《Applied mathematics and computation》2010,216(8):2479-4515
Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2 + 1)-dimensional Sine-Gordon equation, Appl. Math. Comput. 215 (2009) 3777-3781] are analyzed. We have observed that fourteen solutions by Li from 30 do not satisfy the equation. The other 16 exact solutions by Li can be found from the general solutions of the well-known solution of the equation for the Weierstrass elliptic function. 相似文献
6.
In this paper, we investigate Klein-Gordon equation with cubic nonlinearity. All explicit expressions of the bounded travelling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded travelling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution. 相似文献
7.
This paper is concerned with a nonlinear iterative functional differential equation x′(z) = 1/x(p(z) + bx′(z)). By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. We discuss not only in the general case, but also in critical cases, especially for α given in Schröder transformation is a root of the unity. And in case (H4), we dealt with the equation under the Brjuno condition, which is weaker than the Diophantine condition. Moreover, the exact and explicit solution of the original equation has been investigated for the first time. Such equations are important in both applications and the theory of iterations. 相似文献
8.
Juan Dávila Marcelo Montenegro 《Journal of Mathematical Analysis and Applications》2009,352(1):360-379
For the equation
9.
A similarity analysis of a nonlinear fin equation has been carried out by M. Pakdemirli and A.Z. Sahin [Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. (2005) (in press)]. Here, we consider a further group theoretic analysis that leads to an alternative set of exact solutions or reduced equations with an emphasis on travelling wave solutions, steady state type solutions and solutions not appearing elsewhere. 相似文献
10.
11.
Filipe J. Romeiras 《Applied mathematics and computation》2009,215(5):1791-1805
We search for exact travelling wave solutions of the generalized Bretherton equation for integer, greater than one, values of the exponent m of the nonlinear term by two methods: the truncated Painlevé expansion method and an algebraic method. We find periodic solutions for m=2 and m=5, to add to those already known for m=3; in all three cases these solutions exist for finite intervals of the wave velocity. We also find a “kink” shaped solitary wave for m=5 and a family of elementary unbounded solutions for arbitrary m. 相似文献
12.
Exact solutions of Kolmogorov-Petrovskii-Piskunov equation using the modified simple equation method
The modified simple equation method is employed to find the exact solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation. When certain parameters of the equations are chosen to be special values, the solitary wave solutions are derived from the exact solutions. It is shown that the modified simple equation method provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. 相似文献
13.
We study the exact number of positive solutions of the Dirichlet problem for the one-dimensional prescribed mean curvature equation
14.
Shuguan Ji 《Journal of Differential Equations》2018,264(9):5527-5540
This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient satisfies with , which actually excludes the classical constant coefficient model. For the case , it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form ( are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition . 相似文献
15.
A Wick-type stochastic 2D KdV equation with variable coefficients is investigated. The exact solutions are showed by using the homogeneous balance principle and the Herimite transform in the white noise space. 相似文献
16.
Ibrahim E. Inan 《Applied mathematics and computation》2010,217(4):1294-1299
In this paper, we implemented the exp-function method for the exact solutions of the fifth order KdV equation and modified Burgers equation. By using this scheme, we found some exact solutions of the above-mentioned equations. 相似文献
17.
Nikolai A. Kudryashov Dmitry I. Sinelshchikov 《Applied mathematics and computation》2010,217(1):414-421
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions of nonlinear evolution equation of the fourth order are found by means of the simplest equation method. Properties of nonlinear waves in a liquid with gas bubbles are discussed. 相似文献
18.
V.F. Lubyshev 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1345-1354
We study multiple solutions of an even-order nonlinear partial differential equation with a Dirichlet boundary condition. A related class of nonlinear systems is investigated. 相似文献
19.
Hari M. Srivastava Hatira Günerhan Behzad Ghanbari 《Mathematical Methods in the Applied Sciences》2019,42(18):7210-7221
The main aim of this article is to present some new exact solutions of the resonant nonlinear Schrödinger equation. These solutions are derived by using the generated exponential rational function method (GERFM). The kink‐type, bright, dark, and singular soliton solutions are reported, and several numerical simulations are also included. The calculations are carried out by Maple software. All of the solutions that are derived in this paper are believed to be new and have presumably not been reported in earlier publications. 相似文献
20.
Nikolai A. Kudryashov 《Journal of Computational and Applied Mathematics》2010,234(12):3511-3512
Exact solutions of the Kawahara equation by Assas [L.M.B. Assas, New Exact solutions for the Kawahara equation using Exp-function method, J. Comput. Appl. Math. 233 (2009) 97-102] are analyzed. It is shown that all solutions do not satisfy the Kawahara equation and consequently all nontrivial solutions by Assas are wrong. 相似文献