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1.
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   

2.
石玉仁  张娟  杨红娟  段文山 《物理学报》2011,60(2):20402-020402
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   

3.
石玉仁  张娟  杨红娟  段文山 《物理学报》2011,60(2):20401-020401
利用扩展双曲函数法求解了耦合KdV方程,得到了6类精确解,其中一类为具有双峰状结构的单孤子解.在不同的极限情况下,该解分别退化为耦合KdV方程的扭结状或钟状孤波解.文中对双峰孤立波的稳定性进行了数值研究,结果表明:耦合KdV方程的双峰孤立波在长波小振幅扰动和小振幅钟型孤立波扰动下,均稳定. 关键词: 耦合KdV方程 双峰孤立子 稳定性  相似文献   

4.
利用函数展开法求解修正耦合KdV(Coupled KdV,cKdV)方程组,得到几类孤立波解,包括扭结型—钟型、双扭结型、双钟型以及双扭结—双钟型结构的单孤子解.在不同的极限情况下,这些解分别退化为修正cKdV方程的扭结状或钟状孤波解.对孤立波的稳定性进行了数值研究,结果表明:修正cKdV方程既存在稳定的孤立波解,也存在不稳定的孤立波解.  相似文献   

5.
江波  韩修静  毕勤胜 《物理学报》2010,59(12):8343-8347
用动力系统分岔方法研究了一类非线性色散Boussinesq方程.在不同的参数条件下,给出了该方程具有隐函数形式的孤立波解的解析表达式.数值模拟进一步验证了所得结果的正确性.  相似文献   

6.
殷久利  田立新 《物理学报》2009,58(6):3632-3636
研究一类非线性色散广义DGH方程的新型奇异孤立波及其Painlevé可积性.利用Painlevé分析发现当对流项强度m=2时广义DGH方程是可积的,这是一个新的可积方程.通过构造新的变量代换以及auto-Backlund变换获得该方程丰富的奇异孤立波解,如紧孤立波(compacton)、尖峰孤立波(peakon)、新型带尖点的双孤立波和带爆破点的双孤立波等. 关键词: 非线性色散方程 可积性 奇异孤立波  相似文献   

7.
黄令 《物理学报》2006,55(8):3864-3868
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   

8.
BBM方程和修正的BBM方程新的精确孤立波解   总被引:20,自引:0,他引:20       下载免费PDF全文
采用一种双曲函数假设和一类新的辅助常微分方程相结合的方法给出BBM方程和修正的BBM 方程新的精确孤立波解.这种方法也可用于寻找其他非线性发展方程新的孤立波解. 关键词: 辅助方程 双曲函数假设 孤立波解  相似文献   

9.
正弦-高登方程对应的孤立波在非线性物理学中占有重要地位,但它不像孤立水波那样容易产生,它通常发生在微观领域.本文通过一种宏观装置近似演示正弦-高登方程孤立波,在理论上证实了该波为孤立波,研究了该孤立波的稳定发生、波速与碰撞等方面的性质.  相似文献   

10.
孤立波方程的保结构算法   总被引:4,自引:0,他引:4  
王雨顺  王斌  季仲贞 《计算物理》2004,21(5):386-400
讨论了孤立波方程的保结构差分算法,以一些经典的孤立波方程为例,如KdV,sine-Gordon,K-P方程,给出了它们的辛和多辛结构,说明辛和多辛算法的可适用性.提出局部守恒算法和广义保结构算法的概念,它们是保结构算法的概念自然推广.还给出一种能系统构造局部守恒格式的复合方法.数值例子说明,保结构数值能很好模拟各种孤立波的演化。  相似文献   

11.
石玉仁  汪映海  杨红娟  段文山 《物理学报》2007,56(12):6791-6796
利用同伦分析法求解了修正的Kadomtsev-Petviashvili方程, 得到了它的近似孤立波解, 该解与精确解符合得非常好.结果表明,同伦分析法在求解高维非线性演化方程的孤立波解时, 仍然是一种行之有效的方法. 关键词: 同伦分析法 修正的Kadomtsev-Petviashvili方程 孤立波解  相似文献   

12.
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   

13.
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   

14.
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   

15.
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   

16.
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   

17.
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   

18.
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   

19.
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   

20.
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   

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