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1.
The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type.In different regions of the parametric space,sufficient conditions to guarantee the existence of solitary wave solutions,periodic wave solutions,kink and anti-kink wave solutions are given.All possible exact explicit parametric representations are obtained for these waves. 相似文献
2.
By using the theory of bifurcations of planar dynamic systems to the coupled Jaulent-Miodek equations,the existence of smooth solitary travelling wave solutions and uncountably infinite many smooth periodic travelling wave solutions is studied and the bifurcation parametric sets are shown.Under the given parametric conditions,all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained. 相似文献
3.
Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given. 相似文献
4.
李继彬 《应用数学和力学(英文版)》2008,29(4):437-440
By using the method of dynamical systems, the travelling wave solutions of for an integrable nonlinear evolution equation is studied. Exact explicit parametric representations of kink and anti-kink wave, periodic wave solutions and uncountably infinite many smooth solitary wave solutions are given. 相似文献
5.
Introduction FangShaomeiandGuoBoling[1]consideredthefollowingtimeperiodicproblemof dampedcouplednonlinearwaveequations:ut f(u)x-αuxx βuxxx 2vvx=G1(u,v) h1(x),vt-γvxx 2(uv)x g(v)x=G2(u,v) h2(x),(1)whereα,β,γareconstants,andγ>0,β≠0.Undertheperiodicboundaryconditions,the authorsobtainedtheuniqueexistenceofstrongsolutionsfortheabovesystem.InthispaperweshallconsiderbifurcationbehaviorofthetravellingwavesolutionsofEq.(1)inthecaseGi(u,v)≡0,hi(u,v)≡0(i=1,2).Letξ=x-ct,u=u(x-ct),where cis… 相似文献
6.
李继彬 《应用数学和力学(英文版)》2009,30(5):537-547
Dynamical analysis has revealed that, for some nonlinear wave equations, loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loopsoliton solution consists of three solutions, and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a "real" loopsolution exists, and if so, what are the precise parametric representations of these loop traveling wave solutions. 相似文献
7.
By finding a parabola solution connecting two equilibrium points of a planar dynamical system,the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown.Some exact explicit parametric representations of kink wave solutions are given.Explicit parameter conditions to guarantee the existence of kink wave solutions are determined. 相似文献
8.
This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the
Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical
system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given. 相似文献
9.
IntroductionWiththerapiddevelopmentofscienceandtechnology ,thestudykernelofmodernscienceischangedfromlineartononlinearstepbystep .Manynonlinearscienceproblemscansimplyandexactlybedescribedbyusingthemathematicalmodelofnonlinearequation .Uptonow ,manyimpor… 相似文献
10.
In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics. 相似文献
11.
混合流体Rayleigh-Benard对流是研究对流稳定性,时空结构和非线性特性的典型模型之一。本文利用流体力学扰动方程组的数值模拟,讨论了偏离传导状态具有强SORET效应的混合流体行进波对流的温度场和浓度场的成长过程,分析了充分发展对流情况下的对流振幅,Nusselt数及混合参数与相对瑞利数的关系。并给出了行进波相速度对相对瑞利数的依赖关系。结果说明混合参数的曲线与行进波相速度的分布曲线是类似的。文末,给出了垂直速度,温度和浓度场的分布并讨论了相对瑞利数对场的分布及不同场之间的相位差的影响。 相似文献
12.
By using the method of dynamical systems, this paper researches the bifurcation and the exact traveling wave solutions for a (1+2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Exact parametric representations of all wave solutions are given. 相似文献
13.
Michal Fečkan 《Journal of Dynamics and Differential Equations》1998,10(4):605-617
Periodic solutions of abstract, nonlinear, wave equations are given when eigen-values of linear parts of those equations are incommensurable to the time period and a certain parameter is sufficiently large. 相似文献
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李庶民 《应用数学和力学(英文版)》2001,22(11):1333-1343
IntroductionTheexistenceofpeakonTWSofanonlinearwaveequationρt =bux 12 [(u2 ±u2 x) ρ] x, ρ =u±uxx ( 1 )wasconsideredbreiflybyP .Rosenau (see [1 ] ) .Eq.( 1 )isfoundby“reshuffling”Hamiltonianoperatorofbi_HamiltionianstructureinKdVandmKdVequation (see [2 ] ) .BecauseEq.( 1 )hasstron… 相似文献
16.
李继彬 《应用数学和力学(英文版)》2008,29(11):1391-1398
By using the dynamical system method to study the 2D-generalized Benney- Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parametric representations for solutions of kink wave, periodic wave and unbounded traveling wave are obtained. 相似文献
17.
In this paper, we study strongly nonlinear axisymmetric waves in a circular cylindrical rod composed of a compressible Mooney-Rivlin material. To consider the travelling wave solutions for the governing partial differential system, we first reduce it to a nonlinear ordinary differential equation. By using the bifurcation theory of planar dynamical systems, we show that the reduced system has seven periodic annuluses with different boundaries which depend on four parameters. We further consider the bifurcation behavior of the phase portraits for the reduced one-parameter vector fields when other three parameters are fixed. Corresponding to seven different periodic annuluses, we obtain seven types of travelling wave solutions, including solitary waves of radial contraction, solitary waves of radial expansion, solitary shock waves of radial contraction, solitary shock waves of radial expansion, periodic waves and two types of periodic shock waves. These are physically acceptable solutions by the governing partial differential system. The rigorous parameter conditions for the existence of these waves are given. 相似文献
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19.
James P. Denier Jillian A.K. Stott Eunice W. Mureithi 《Theoretical and Computational Fluid Dynamics》1998,10(1-4):105-114
We consider nonlinear wave motions in strongly buoyant mixed forced–free convection boundary layer flows. In the natural
limit of large Reynolds number the nonlinear evolution of a single monochromatic wave mode is shown to be governed by a novel
wave/mean-flow interaction in which the wave amplitude and the wave induced mean-flow are of comparable size. A nonlinear
integral equation describing the bifurcation to finite-amplitude travelling wave solutions is derived. Solutions of this equation
are presented together with a discussion of their physical significance.
Received 10 December 1996 and accepted 14 April 1997 相似文献
20.
Henri Berestycki Bernard Larrouturou Jean -Michel Roquejoffre 《Archive for Rational Mechanics and Analysis》1992,117(2):97-117
We investigate the stability of travelling wave solutions of the multidimensional thermodiffusive model for flame propagation with unit Lewis number. This model consists in a system of two nonlinear parabolic equations posed in an infinite cylinder, with Neumann boundary conditions. In this paper, we prove that every travelling wave solution of this model is linearly stable. Our tools are exponential decay estimates for solutions of elliptic equations in a cylinder, and the Maximum Principle for parabolic equations. 相似文献