共查询到20条相似文献,搜索用时 15 毫秒
1.
利用双曲函数型假设与两个辅助常微分方程相结合及吴代数消元法给出了BBM和(2+1)维BBM方程一些新的精确解孤波解. 相似文献
2.
In this paper the Green’s function method and results about fixed point are used to get existence results on periodic traveling wave solution for non-homogeneous problems of generalized versions of the BBM and KdVB equations. It is shown through the constructions of explicit Green’s functions that the periodic boundary value problems for the traveling wave solutions of the BBM and KdVB equations are equivalent to integral equations which generate compact operators in the space of periodic functions. These integral representations allowed us to prove that if the speed of the wave propagation is suitably chosen, then the BBM and KdVB equations will admit periodic traveling wave solution. 相似文献
3.
杨昆望 《纯粹数学与应用数学》2012,(1):85-91
利用指数函数展开法,研究BBM方程与KG方程,在一个特定的变换下,借助Maple软件的符号运算功能,获得BBM方程与KG方程指数函数型新的孤立波解与周期解.这种方法用于求解非线性发展方程是简单而有效的. 相似文献
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5.
Xiaofang Duan Junliang Lu Yaping Ren Rui Ma 《Journal of Nonlinear Modeling and Analysis》2022,4(4):628-649
The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional
propagation of nonlinear dispersive long waves, which has a clear
physical background, and is a more suitable mathematical and
physical equation than the KdV equation. Therefore, the research
on the BBM equation is very important. In this article, we put
forward an effective algorithm, the modified hyperbolic function
expanding method, to build the solutions of the BBM equation. We, by
utilizing the modified hyperbolic function expanding method,
obtain the traveling wave solutions of the BBM equation.
When the parameters are taken as special values, the solitary
waves are also derived from the traveling waves. The traveling
wave solutions are expressed by the hyperbolic functions, the
trigonometric functions and the rational functions. The modified
hyperbolic function expanding method is direct, concise, elementary
and effective, and can be used for many other nonlinear partial
differential equations. 相似文献
6.
A.S. Abdel Rady 《Applied mathematics and computation》2010,217(4):1385-1390
We make use of the homogeneous balance method and symbolic computation to construct new exact traveling wave solutions for the Benjamin-Bona-Mahoney (BBM) equation. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations. 相似文献
7.
In this paper, a method with the aid of a sub-ODE and its solutions is used for constructing new periodic wave solutions for nonlinear Gardner equation and BBM equation with nonlinear terms of any order arising in mathematical physics. As a result, many exact traveling wave solutions are successfully obtained. The method in the paper is very direct and it can also be applied to other nonlinear evolution equations. 相似文献
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新型广义BBM方程B(m,n)的孤立波模型解 总被引:1,自引:1,他引:0
王丽霞 《数学的实践与认识》2006,36(10):259-262
引进了一类带强色散项的新型广义BBM方程B(m,n):ut+ux+a(um)x+b(un)xx t=0,研究了B(m,n)方程的孤立波模型解,分别得到了它的双曲正弦,双曲余弦,双曲正切形式的孤立波模型解. 相似文献
10.
Based on the homogeneous balance method,the Jacobi elliptic expansion method and the auxiliary equation method,the first elliptic function equation is used to get a new kind of solutions of nonlinear evolution equations.New exact solutions to the Jacobi elliptic function of MKdV equations and Benjamin-Bona-Mahoney (BBM) equations are obtained with the aid of computer algebraic system Maple.The method is also valid for other (1+1)-dimensional and higher dimensional systems. 相似文献
11.
该文推导了具任意次非线性项的Liénard方程a″(ξ)+la(ξ)+ma\+q(ξ)+na\+\{2q-1\}(ξ)=0和\{a″(ξ)\}+ra′(ξ)+la(ξ)+ma\+q(ξ)+na\+\{2q-1\}(ξ)=0解的若干性质,通过适当变换,并结合假设待定法求出了它们的钟状和扭状显式精确解.据此,求出了一批具任意次非线性项的发展方程的钟状和扭状显式精确孤波解,其中包括广义BBM型方程、二维广义Klein Gordon方程、广义Pochhammer Chree方程和非线性波方程等. 相似文献
12.
Traveling wave solutions for fractional partial differential equations arising in mathematical physics by an improved fractional Jacobi elliptic equation method 总被引:1,自引:0,他引:1 下载免费PDF全文
In this paper, combining with a new generalized ansätz and the fractional Jacobi elliptic equation, an improved fractional Jacobi elliptic equation method is proposed for seeking exact solutions of space‐time fractional partial differential equations. The fractional derivative used here is the modified Riemann‐Liouville derivative. For illustrating the validity of this method, we apply it to solve the space‐time fractional Fokas equation and the the space‐time fractional BBM equation. As a result, some new general exact solutions expressed in various forms including the solitary wave solutions, the periodic wave solutions, and Jacobi elliptic functions solutions for the two equations are found with the aid of mathematical software Maple. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
13.
Lionel Rosier 《数学研究》2016,49(2):195-204
We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback
law, or a boundary feedback law. In each case, we prove the global well-posedness
of the system and the convergence towards a solution of the BBM equation which is
null on a band. If the Unique Continuation Property holds for the BBM equation, this
implies that the origin is asymptotically stable for the damped BBM equation. 相似文献
14.
Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations. 相似文献
15.
This paper combines the bifurcation theory of dynamical systems and the Fan sub-equation method to improve the Fan sub-equation method for solving the BBM equation. Periodic solutions, kink solutions and solitary solutions are formally derived in a general form. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations. 相似文献
16.
Lei Zeng 《Journal of Differential Equations》2003,188(1):1-32
We consider solitary-wave solutions of equations of Benjamin-Bona-Mahony type. We show that for a large class of equations of BBM type, there do exist stable sets consisting of solitary-wave profile functions. In the case of generalized BBM equations, we found that there are profile functions of stable solitary waves that are not the minimizers of the associated variational problem. Such a phenomenon is not known to exist for equations of Korteweg-de Vries type. 相似文献
17.
This paper discusses the existence and stability of solitary-wave solutions
of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves
pseudo-differential operators for the linear part. One of such equations can be derived
from water-wave problems as second-order approximate equations from fully nonlinear
governing equations. Under some conditions on the symbols of pseudo-differential
operators and the nonlinear terms, it is shown that the general higher-order BBM equation
has solitary-wave solutions. Moreover, under slightly more restrictive conditions,
the set of solitary-wave solutions is orbitally stable. Here, the equation has a nonlinear
part involving the polynomials of solution and its derivatives with different degrees
(not homogeneous), which has not been studied before. Numerical stability and instability
of solitary-wave solutions for some special fifth-order BBM equations are also
given. 相似文献
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19.
The Lie-group formalism is applied to investigate the symmetries of the Benjamin-Bona-Mahony (BBM) equation with variable coefficients. We derive the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained. 相似文献
20.
《Communications in Nonlinear Science & Numerical Simulation》2005,10(2):133-138
In this paper, based on a variable-coefficient balancing-act method, by means of an appropriate transformation and with the help of Mathematica, we obtain some new types of solitary-wave solutions to the generalized Benjamin–Bona–Mahony (BBM) equation and the generalized Burgers–Fisher (BF) equation with nonlinear terms of any order. These solutions fully cover the various solitary waves of BBM equation and BF equation previously reported. 相似文献