共查询到20条相似文献,搜索用时 78 毫秒
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采用双曲函数展开法得到Modified Benjamin-Bona-Mahony(mBBM)方程的一类扭结-反扭结状的双扭结孤立波解,在不同的极限情况下,此孤立波分别退化为mBBM方程的扭结状和钟状孤立波解.对双扭结型单孤子的结构特征进行分析,构造有限差分格式对其动力学稳定性进行数值研究.有限差分格式为两层隐式格式,在线性化意义下无条件稳定.数值结果表明mBBM方程的双扭结型单孤子在不同类型的扰动下均具有很强的稳定性.对双孤立波的碰撞进行数值模拟,发现既存在弹性碰撞也存在非弹性碰撞. 相似文献
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利用扩展的双曲函数法得到了combined KdV-mKdV (cKdV)方程的几类精确解,其中一类为具有扭结—反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为cKdV方程的扭结状或钟状孤波解.理论分析表明,cKdV方程既有传播型孤立波解,也有非传播型孤立波解.文中对双扭结型孤立波解的稳定性进行了数值研究,结果表明,cKdV方程既存在稳定的双扭结型孤立波,也存在不稳定的双扭结型孤立波.
关键词:
cKdV方程
双扭结单孤子
稳定性 相似文献
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对称性分析是自然科学研究中的重要方法之一. 利用对称性分析研究了一个描述两层流体体系的模型即耦合Burgers方程的对称性. 利用对称性给出了这个模型的四种对称性约化并给出了这些约化方程的一些特殊的严格解,如有理解、行波孤立子解和非行波孤立子解.
关键词:
对称性约化
耦合Burgers方程
孤立子 相似文献
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A. V. Porubov 《Technical Physics》2005,50(7):864-867
A 2D generalized Gardner equation is used to describe 2D nonlinear internal waves in a two-layer fluid. Unlike the previous model based on the Kadomtsev-Petviashvili equation, the model considered here allows for the instability of a plane internal solitary wave. Such a possibility causes the wave to be localized in any direction. Relationships between the thicknesses and densities of the layers under the instability conditions are obtained. 相似文献
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Amin Esfahani 《Physics letters. A》2010,374(35):3635-3645
In this Letter, the existence of the solitary wave solution of the Kadomtsev-Petviashvili equation with generalized evolution and time-dependent coefficients will be studied. We use the solitary wave ansätze-method to derive these solutions. A couple of conserved quantities are also computed. Moreover, some figures are plotted to see the effects of the coefficient functions on the propagation and asymptotic characteristics of the solitary waves. 相似文献
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As is well known, Korteweg-de Vries equation is a typical one which has planar solitary wave. By considering higher order
transverse disturbance to planar solitary waves, we study a Kadomtsev-Petviashvili (KP) equation and find some interesting
results. In this letter we investigate the three soliton interaction and their resonance phenomena of KP equation, and theoretically
find that the maximum amplitude is 9 times of the initial interacting soliton for three same amplitude solitions. Three arbitrary
amplitude solition interaction of KP equation is also studied by numerical simulation, which can also results in resonance
phenomena. 相似文献
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Decay of the local energy of a two-dimensional wave in a nonlinear weakly negative dispersive medium
Wojciech Gawlik 《Physics letters. A》1982,90(6):278-279
We show that the local energy of a two-dimensional wave in a nonlinear weakly negative dispersive medium which is described by a modified Kadomtsev-Petviashvili equation decays to zero as time goes to infinity. 相似文献
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Nonlinear electromagnetic wave propagation through cold collisionless plasma in (2+1) dimensions is studied using the nonlinear
reductive perturbation method. It is shown that to the lowest order of perturbation, the system of equations can be reduced
to modified Kadomtsev-Petviashvili equation. 相似文献
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Recently,a report from Elite Readers suggested that a strange phenomenon of 'square-shaped waves' had occurred at the beaches of the Isle of Rhe in the Bay of Biscay.Based on the hydrological and geological data of the Bay of Biscay,we find that the special phenomenon is closely related to a solitary wave that can be described by the shallow water wave equation.We discuss the formation mechanisms of the square-shaped waves by the Kadomtsev-Petviashvili equation.The combination of exact solutions and actual condition provides the simulated initial state.We then reproduce a square-shaped structure by a numerical method and obtain the result consistent with the observed picture from media.Our work enriches public understanding of strange water waves and has great significance for tourism development and shipping transportation. 相似文献
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A collocation method based on an extended cubic B-spline function is introduced for the numerical solution of the modified regularized long wave equation. The accuracy of the method is illustrated by studying the single solitary wave propagation and the interaction of two solitary waves of the modified regularized long wave equation. 相似文献
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The linear stability of planar solitary waves with respect to long-wavelength transverse perturbations is studied in the framework of the generalized Kadomtsev-Petviashvili equation. It is newly discovered that for some nonlinearities in this family, the solitary waves could be transversely unstable even in a medium with negative dispersion. In the case of positive dispersion, they are found to be always unstable. 相似文献
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We prove that the set of solitary wave solutions of a generalized Kadomtsev-Petviashvili equation in two dimensions, (u
t+(um+1)x+uxxx)x=uyy is stable for 0<m<4/3. 相似文献