共查询到20条相似文献,搜索用时 15 毫秒
1.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(7):1759-1764
In this paper, we use the first integral method for analytic treatment of the modified Benjamin–Bona–Mahony equation. Some exact new solutions are formally derived. 相似文献
2.
Mohammed Khalfallah 《Mathematical and Computer Modelling》2009,49(3-4):666-671
The extended homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq–Burgers equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Boussinesq–Burgers equation are successfully obtained. 相似文献
3.
In this paper, we study the optimal decay rates of solutions for the generalized Benjamin–Bona–Mahony equation in multi-dimensional space (n≥3). By using Fourier transform and the energy method, we obtain the Lq(2≤q≤∞) convergence rates of the solutions under the condition that the initial data is small. The optimal decay rates obtained in this paper are found to be the same as the decay rate for the Heat equation. 相似文献
4.
A. Rashid 《Journal of Mathematical Sciences》2009,160(1):84-94
In this paper, we consider the spectral collocation method for the Ginzburg–Landau equation coupled with the Benjamin–Bona–Mahony
equation. Semidiscrete and fully discrete spectral collocation schemes are given. In the fully discrete case, a three-level
spectral collocation scheme is considered. An energy estimation method is used to obtain error estimates for the approximate
solutions.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal
Conference–2006, Part 3, 2008. 相似文献
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6.
Kamruzzaman Khan M. Ali Akbar Md. Nur Alam 《Journal of the Egyptian Mathematical Society》2013,21(3):233-240
In this paper, the modified simple equation (MSE) method is implemented to find the exact solutions for the nonlinear Drinfel’d–Sokolov–Wilson (DSW) equation and the modified Benjamin–Bona–Mahony (mBBM) equations. The efficiency of this method for constructing these exact solutions has been demonstrated. It is shown that the MSE method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this technique reduces the large volume of calculations. 相似文献
7.
Hui Yin Shuyue Chen Jing Jin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,1(2):969-1001
This paper is concerned with the large time behavior of traveling wave solutions to the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers
equations
$u_t- u_{txx}- vu_{xx}+\beta u_x+f(u)_x = 0,\, t > 0,\, x \in {\bf R}\quad\quad ({\rm E})$u_t- u_{txx}- vu_{xx}+\beta u_x+f(u)_x = 0,\, t > 0,\, x \in {\bf R}\quad\quad ({\rm E}) 相似文献
8.
Hui Yin Shuyue Chen Jing Jin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(6):969-1001
This paper is concerned with the large time behavior of traveling wave solutions to the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers
equations
9.
10.
The concept of nonlinear self-adjointness given by Ibragimov is applied to a Generalized Benjamin–Bona–Mahony–Burgers equation. Then, a nonlinear self-adjoint classification has been achieved. Moreover, some nontrivial conservation laws are constructed by using the multipliers method which does not require the use of a variational principle. Finally, by applying the modified simplest equation method we derive new travelling wave solutions. 相似文献
11.
Qifeng
Zhang Lingling Liu Jiyuan Zhang 《Numerical Methods for Partial Differential Equations》2020,36(6):1790-1810
In the article, two linearized finite difference schemes are proposed and analyzed for the Benjamin–Bona–Mahony–Burgers (BBMB) equation. For the construction of the two-level scheme, the nonlinear term is linearized via averaging k and k + 1 floor, we prove unique solvability and convergence of numerical solutions in detail with the convergence order O(τ2 + h2) . For the three-level linearized scheme, the extrapolation technique is utilized to linearize the nonlinear term based on ψ function. We obtain the conservation, boundedness, unique solvability and convergence of numerical solutions with the convergence order O(τ2 + h2) at length. Furthermore, extending our work to the BBMB equation with the nonlinear source term is considered and a Newton linearized method is inserted to deal with it. The applicability and accuracy of both schemes are demonstrated by numerical experiments. 相似文献
12.
In this article, we consider Benjamin–Bona–Mahony equation with a time delay. By using the Liapunov function method, we show that the time-delayed Benjamin–Bona–Mahony equation is exponentially decay if the delay parameter is sufficiently small. 相似文献
13.
Recently, Zhu et al. (2020) proposed a kind of rotation-Camassa–Holm equation. In this paper, we study the question of nonexistence of periodic peaked traveling wave solution for rotation-Camassa–Holm equation. Indeed, rotation-Camassa–Holm equation has no nontrivial periodic Camassa–Holm peaked solution unlike Camassa–Holm equation, modified Camassa–Holm equation, Novikov equation. 相似文献
14.
15.
Chaosheng Zhu 《Applicable analysis》2013,92(1):59-65
We utilize a new necessary and sufficient condition to verity the asymptotic compactness of an evolution equation defined in an unbounded domain, which involves the Littlewood–Paley projection operators. We then use this condition to prove the existence of an attractor for the damped Benjamin–Bona–Mahony equation in the phase space H 1(R 1) by showing the solutions are point dissipative and asymptotically compact. Moreover the attractor is in fact smoother and it belongs to H 3/2?? for every ?>0. 相似文献
16.
By using the method of dynamical systems, the travelling wave solutions of a special CH–DP equation are studied. Exact explicit parametric representations of smooth solitary waves, solitary cusp waves, breaking waves and uncountably infinitely many smooth periodic wave solutions are given. In different regions of the parametric plane, different phase portraits are determined. The so called loop soliton solution is discussed. 相似文献
17.
In this paper, we generalize the exp-function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations, to nonlinear differential–difference equations (NDDEs). As an illustration, two series of exact travelling wave solutions of the discrete sine–Gordon equation are obtained by means of the exp-function method. As some special examples, these new exact travelling wave solutions can degenerate into the kink-type solitary wave solutions reported in the open literature. 相似文献
18.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(10):3956-3963
A two-component Fornberg–Whitham equation is introduced as a model for water waves. The bifurcations of traveling wave solutions are studied. Parametric conditions to smooth soliton solution, kink solution, antikink solution and uncountable infinite many smooth periodic wave solutions are given. Some expressions for those solutions are presented. 相似文献
19.
In this paper, we consider the global existence as well as the optimal decay estimates of the Cauchy problem for the multi-dimensional Benjamin–Bona–Mahony–Burgers equation with large initial data in the whole-space. And these results are obtained by Green?s function method, Fourier analysis method, energy estimates method combined with the time-frequency decomposition method. 相似文献
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