共查询到19条相似文献,搜索用时 109 毫秒
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对于一类KdV方程的孤子解和一类KdV-Burgers方程的行波解,利用直接扰动法证明了它们具有条件稳定性,即解的稳定性敏感的依赖于方程的参数和初始条件,从而推广和修正了近期文献中关于这些解不稳定的结论.
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证明了KdV型议程的孤波解和KdV-Burgers型方程的行波解在李亚诺夫意义下是不是稳定的,从而修正了文献中的一些结论。 相似文献
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扩展齐次平衡法与Backlund变换 总被引:1,自引:0,他引:1
将求解非线性演化方程的齐次平衡法进行了扩展,使其包含一个任意函数.此改进方法可得到耦合KdV-Burgers方程、KdV-Burgers方程、Boussinesq方程和一般KdV方程等许多非线性演化方程的Backlund变换和新的精确解. 相似文献
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We consider a two-component system of reaction-diffusion equations with a
small cutoff in the reaction term. A semi-analytical solution of fronts and how the front velocities vary with the parameters
are given for the case when the system has a piecewise linear nonlinearity.
We find the existence of a nonequilibrium Ising-Bloch bifurcation for the front speed when the cutoff is present. Numerical
results of solutions to these equations are also presented and they allow us to consider the collision between fronts, and
the existence of different types of traveling
waves emerging from random initial conditions. 相似文献
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John David Crawford 《Journal of statistical physics》1994,74(5-6):1047-1084
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and we apply center-manifold reduction to obtain the amplitude equations for steady-state and Hopf bifurcation from the equilibrium state with a uniform phase distribution. When the population is described by a native frequency distribution that is reflection-symmetric about zero, the problem has circular symmetry. In the limit of zero extrinsic noise, although the critical eigenvalues are embedded in the continuous spectrum, the nonlinear coefficients in the amplitude equation remain finite, in contrast to the singular behavior found in similar instabilities described by the Vlasov-Poisson equation. For a bimodal reflection-symmetric distribution, both types of bifurcation are possible and they coincide at a codimension-two Takens-Bogdanov point. The steady-state bifurcation may be supercritical or subcritical and produces a time-independent synchronized state. The Hopf bifurcation produces both supercritical stable standing waves and supercritical unstable traveling waves. Previous work on the Hopf bifurcation in a bimodal population by Bonilla, Neu, and Spigler and by Okuda and Kuramoto predicted stable traveling waves and stable standing waves, respectively. A comparison to these previous calculations shows that the prediction of stable traveling waves results from a failure to include all unstable modes. 相似文献
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Existence of traveling waves propagating without internal reflection in inclined water channels of arbitrary slope is demonstrated. It is shown that traveling non-monochromatic waves exist in both linear and nonlinear shallow water theories in the case of a uniformly inclined channel with a parabolic cross-section. The properties of these waves are studied. It is shown that linear traveling waves should have a sign-variable shape. The amplitude of linear traveling waves in a channel satisfies the same Green's law, which is usually derived from the energy flux conservation for smoothly inhomogeneous media. Amplitudes of nonlinear traveling waves deviate from the linear Green's law, and the behavior of positive and negative amplitudes are different. Negative amplitude grows faster than positive amplitude in shallow water. The phase of nonlinear waves (travel time) is described well by the linear WKB approach. It is shown that nonlinear traveling waves of any amplitude always break near the shoreline if the boundary condition of the full absorption is applied. 相似文献
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Dynamical System Approach to a Coupled Dispersionless System: Localized and Periodic Traveling Waves 下载免费PDF全文
Gambo Betchewe Kuetche Kamgang Victor Bouetou Bouetou Thomas Timoleon Crepin Kofane 《中国物理快报》2009,26(6):55-57
We investigate the dynamical behavior of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following a dynamical system approach, we unwrap typical miscellaneous traveling waves including localized and periodic ones. Studying the relative stabilities of such structures through their energy densities, we find that under some boundary conditions, localized waves moving in positive directions are more stable than periodic waves which in contrast stand for the most stable traveling waves in another boundary condition situation. 相似文献
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H.D. Park 《Journal of sound and vibration》2008,315(3):556-568
In order to investigate further nonlinear asymmetric vibrations of a clamped circular plate under a harmonic excitation, we reexamine a primary resonance, studied by Yeo and Lee [Corrected solvability conditions for non-linear asymmetric vibrations of a circular plate, Journal of Sound and Vibration 257 (2002) 653-665] in which at most three stable steady-state responses (one standing wave and two traveling waves) are observed to exist. Further examination, however, tells that there exist at most five stable steady-state responses: one standing wave and four traveling waves. Two of the traveling waves lose their stability by Hopf bifurcation and have a sequence of period-doubling bifurcations leading to chaos. When the system has five attractors: three equilibrium solutions (one standing wave and two traveling waves) and two chaotic attractors (two modulated traveling waves), the basin boundaries of the attractors on the principal plane are obtained. Also examined is how basin boundaries of the modulated motions (quasi-periodic and chaotic motions) evolve as a system parameter varies. The basin boundaries of the modulated motions turn out to have the fractal nature. 相似文献
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D. Z. Li X. D. Xu Z. H. Cong J. Zhang D. Y. Tang D. H. Zhou C. T. Xia F. Wu J. Xu 《Applied physics. B, Lasers and optics》2011,102(1):53-58
A generic nonlocal nonlinear optical system with a diffusive type of nonlinearity is investigated analytically, using the
homogeneous balance principle and the F-expansion technique. Exact traveling wave and soliton solutions are discovered. Numerical
simulation of their propagation and interaction properties is carried out. Our results demonstrate that the nonlocal solitary
waves can be manipulated and controlled by changing the nonlocality parameter. 相似文献
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This paper reviews results about the existence of spatially localized waves in nonlinear chains of coupled oscillators, and provides new results for the Fermi-Pasta-Ulam (FPU) lattice. Localized solutions include solitary waves of permanent form and traveling breathers which appear time periodic in a system of reference moving at constant velocity. For FPU lattices we analyze the case when the breather period and the inverse velocity are commensurate. We employ a center manifold reduction method introduced by Iooss and Kirchgassner in the case of traveling waves, which reduces the problem locally to a finite dimensional reversible differential equation. The principal part of the reduced system is integrable and admits solutions homoclinic to quasi-periodic orbits if a hardening condition on the interaction potential is satisfied. These orbits correspond to approximate travelling breather solutions superposed on a quasi-periodic oscillatory tail. The problem of their persistence for the full system is still open in the general case. We solve this problem for an even potential if the breather period equals twice the inverse velocity, and prove in that case the existence of exact traveling breather solutions superposed on an exponentially small periodic tail. 相似文献
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参照板中兰姆波模式的子波叠加解求解了矩形截面固体波导中弹性导波的模式。其中子波设定为横向满足自由边界反射条件、纵向波数分量相同的各板波模式。假设声场的完备性,利用子波模式的正交性,结合矩形截面的几何对称性可以得到4组独立导波特征方程用于频散曲线以及导波模式计算,其计算结果与有限元法计算结果相符。研究以解析模型表明:矩形截面固体波导中的导波是其内部以一定纵向波数分量斜向传播的板波模式在两个自由侧面上经过反复反射与模式转化后,横向耦合谐振而形成的。 相似文献
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Non-linear flexural waves in thin plates or layers have been analyzed in this paper. The equation of motion of the plate is derived assuming that the motion is antisymmetric about the mid-plane of the plate and that the plate is thin. The plate is considered to be elastic. The Von Karman non-linear strains and Landau elastic constants have been used to model geometric and material non-linearities, respectively. An asymptotic analysis of wave motion is presented using the method of multiple scales. Evolution equations are derived for small amplitude traveling flexural elastic waves. Numerical results show waveform distortion, amplitude amplification, and harmonic generation. 相似文献