In this paper, we prove the existence of the pullback attractor for the nonautonomous Benjamin-Bona-Mahony equations in H2 by establishing the pullback uniformly asymptotical compactness.
In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Compa...In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Comparison with Adomian’s decomposition method, homotopy perturbation method, and with the exact solution shows that VHPM is more effective and accurate than ADM and HPM, and is reliable and manageable for this type of equation.展开更多
Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-...Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation is this kind of equation,</span></span></span><span><span><b><span style="font-family:""> </span></b></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">t</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">he solutions are very interest. Several new exact solutions for the nonlinear equation are obtained by using truncated expansion method in this paper. The numerical simulations with different parameters for the new exact solutions of Benjamin</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation are given.</span></span></span>展开更多
In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimati...In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.展开更多
The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C（[0, ∞） × R） ∩ L~∞（[0, ∞）; H1（R）） under the condition that its initial value ...The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C（[0, ∞） × R） ∩ L~∞（[0, ∞）; H1（R）） under the condition that its initial value belongs to the space H1（R）. A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.展开更多
In this paper,we show the existence of pullback attractors for the nonautonomous Benjamin-Bona-Mahony equations by establishing the pullback uniform asymptotically compactness.
In order to get the traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, it is reduced to an ordinary differential equation (ODE) under the travelling wave transformation first. T...In order to get the traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, it is reduced to an ordinary differential equation (ODE) under the travelling wave transformation first. Then complete discrimination system for polynomial is applied to the ZK-BBM equation. The traveling wave solutions of the equation can be obtained.展开更多
基金supported by the NSF of China(11031003, 10871040)
文摘In this paper, we prove the existence of the pullback attractor for the nonautonomous Benjamin-Bona-Mahony equations in H2 by establishing the pullback uniformly asymptotical compactness.
文摘In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Comparison with Adomian’s decomposition method, homotopy perturbation method, and with the exact solution shows that VHPM is more effective and accurate than ADM and HPM, and is reliable and manageable for this type of equation.
文摘Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation is this kind of equation,</span></span></span><span><span><b><span style="font-family:""> </span></b></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">t</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">he solutions are very interest. Several new exact solutions for the nonlinear equation are obtained by using truncated expansion method in this paper. The numerical simulations with different parameters for the new exact solutions of Benjamin</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation are given.</span></span></span>
文摘In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.
文摘The existence of global weak solutions for a generalized Benjamin-Bona-MahonyBurgers equation is established in the space C（[0, ∞） × R） ∩ L~∞（[0, ∞）; H1（R）） under the condition that its initial value belongs to the space H1（R）. A one-sided super bound estimate and a space-time higher-norm estimate on the first order derivatives of the solution with respect to the space variable are derived to prove the existence.
文摘In this paper,we show the existence of pullback attractors for the nonautonomous Benjamin-Bona-Mahony equations by establishing the pullback uniform asymptotically compactness.
文摘In order to get the traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, it is reduced to an ordinary differential equation (ODE) under the travelling wave transformation first. Then complete discrimination system for polynomial is applied to the ZK-BBM equation. The traveling wave solutions of the equation can be obtained.
