共查询到20条相似文献,搜索用时 187 毫秒
1.
《中国科学A辑(英文版)》2007,(1)
Recently, many authors have studied the following CH-γequation: ut c0ux 3uux -α2(wxxt uuxxx 2uxuxx) 4-γuxxx = 0,whereα2, c0 andγare paramters. Its bounded wave solutions have been investigated mainly for the caseα2 > 0. For the caseα2 < 0, the existence of three bounded waves (regular solitary waves, compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given. In this paper, not only the existence of four types of bounded waves: periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the caseα2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results. 相似文献
2.
JiBin Li 《中国科学A辑(英文版)》2008,51(9):1577-1592
Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. 相似文献
3.
In this paper, we study some generalized Camassa-Holm equation. Through the analysis of the phase-portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave and compactons were discussed. In some certain parametric conditions, many exact solutions to the above travelling waves were given. Further-more, the 3D and 2D pictures of the above travelling wave solutions are drawn using Maple software. 相似文献
4.
BIFURCATIONS AND NEW EXACT TRAVELLING WAVE SOLUTIONS OF THE COUPLED NONLINEAR SCHRDINGER-KdV EQUATIONS 下载免费PDF全文
By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions. 相似文献
5.
Exact traveling wave solutions and dynamical behavior for the (n+1)-dimensional multiple sine-Gordon equation 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,(2)
Using the methods of dynamical systems for the (n 1)-dimensional multiple sine-Gordon equation, the existences of uncountably infinite many periodic wave solutions and breaking bounded wave solutions axe obtained. For the double sine-Gordon equation, the exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined. 相似文献
6.
Xie Shaolong 《Annals of Differential Equations》2007,23(1):96-103
We study peaked wave solutions of a generalized Hyperelastic-rod wave equation describing waves in compressible hyperelastic-rods by using the bifurcation theory of planar dynamical systems and numerical simulation method. The existence domain of the peaked solitary waves are found. The analytic expressions of peaked solitary wave solutions are obtained. Our numerical simulation and qualitative results are identical. 相似文献
7.
Bifurcation of travelling wave solutions for (2+1)-dimension nonlinear dispersive long wave equation
In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for (2+1)-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurcation parameter sets are shown,and under various parameter conditions,all exact explicit formulas of solitary travelling wave solutions and kink travelling wave solutions and periodic travelling wave solutions are listed. 相似文献
8.
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived. 相似文献
9.
王明亮 《数学物理学报(B辑英文版)》1988,(1)
First, all possible traveling wave solutions of the Boussinesq equations in shallow water theory are discussed. It is shown that these solutions are periodic waves, convex solitary waves and concave solitary waves. Second, by using a reductive perturbation method, shallow water equation with a small damping term have been reduced to a single KdV-Burgers equation, from which the approximate solution of the original equations can be expressed. 相似文献
10.
By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed. 相似文献
11.
Y. Mammeri 《Acta Appl Math》2012,117(1):1-13
We study the periodic solution of a perturbed regularized Boussinesq system (Bona et al., J. Nonlinear Sci. 12:283–318, 2002, Bona et al., Nonlinearity 17:925–952, 2004), namely the system η
t
+u
x
+β(−η
xxt
+u
xxx
)+α((ηu)
x
+ηη
x
+uu
x
)=0,u
t
+η
x
+β(η
xxx
−u
xxt
)+α((ηu)
x
+ηη
x
+uu
x
)=0, with 0<α,β≤1. We prove that the solution, starting from an initial datum of size ε, remains smaller than ε for a time scale of order (ε
−1
α
−1
β)2, whereas the natural time is of order ε
−1
α
−1
β. 相似文献
12.
In this work we prove that the initial value problem of the Benney-Lin equation ut + uxxx + β(uxx + u xxxx) + ηuxxxxx + uux = 0 (x ∈ R, t ≥0 0), where β 〉 0 and η∈R, is locally well-posed in Sobolev spaces HS(R) for s ≥ -7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain. 相似文献
13.
In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u
t
+u
xxx
+uu
x
)
x
−u
yy
=0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based
upon the application of singular perturbation techniques. 相似文献
14.
Recently, many authors have studied the following CH-γ equation:ut + c0ux + 3uux - α2(uxxt + uuxxx + 2uxuxx) + γuxxx =0,where α2, c0 and γ are paramters. Its bounded wave solutions have been investigated mainly for the case α2 > 0. For the case α2 < 0, the existence of three bounded waves (regular solitary waves,compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given.In this paper, not only the existence of four types of bounded waves: periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the case α2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results. 相似文献
15.
Stephanos Venakides 《纯数学与应用数学通讯》1985,38(2):125-155
The inverse scattering method is used to determine the distribution limit as ? → 0 of the solution u(x, t, ?) of the initial value problem. Ut ? 6uux + ?2uxxx = 0, u(x, 0) = v(x), where v(x) is a positive bump which decays sufficiently fast as x x→±α. The case v(x) ? 0 has been solved by Peter D. Lax and C. David Levermore [8], [9], [10]. The computation of the distribution limit of u(x, t, ?) as ? → 0 is reduced to a quadratic maximization problem, which is then solved. 相似文献
16.
We consider the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation u
t
−u
txx
+2u
x
+3uu
x
=2u
x
u
xx
+uu
xxx
on the half-line x≥0. In this article, we aim to provide a characterization of the solution of the IBV problem in terms of the solution of a
matrix Riemann–Hilbert (RH) factorization problem in the complex plane of the spectral parameter. The data of this RH problem
are determined in terms of spectral functions associated to initial and boundary values of the solution. The construction
requires more boundary data than those needed for a well-posed IBV problem. Their dependence is expressed in terms of an algebraic
relation to be satisfied by the spectral functions. This RH formulation gives us the long-time asymptotics of a solution of
the CH-equation.
Dedicated to Gennadi Henkin in great admiration. 相似文献
17.
John W. Miles 《Studies in Applied Mathematics》1979,60(1):59-72
The asymptotic solution of the Korteweg-de Vries equation uτ + ?uxxx + 2uux = 0 for initial conditions from which no solitons evolve is obtained as a slowly varying similarity solution of the form τ?2/3(Vz?V2, where V = V(z/τ) and z = τ?1/3x. The results are consistent with, but go somewhat beyond, those recently obtained by Ablowitz and Segur [2] through a rather different approach. 相似文献
18.
By using the bifurcation theory of planar dynamical systems to a generalized Camassa–Holm equation
mt+c0ux+umx+2mux=-γuxxx