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《物理学报》2020,(1)
Boussinesq方程是流体力学等领域一个非常重要的方程.本文推导了Boussinesq方程的Lax对.借助于截断Painlevé展开,得到了Boussinesq方程的自B?cklund变换,以及Boussinesq方程和Schwarzian形式的Boussinesq方程之间的B?cklund变换.探讨了Boussinesq方程的非局域对称,研究了Boussinesq方程的单参数群变换和单参数子群不变解.运用Riccati展开法研究了Boussinesq方程,证明Boussinesq方程具有Riccati展开相容性,得到了Boussinesq方程的孤立波-椭圆余弦波解. 相似文献
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本文给出了求解劝边界Boussinesq方程的差分格式,计算了动边界以不同形式运动时所产生的波。数值结果表明了孤立波解的存在。 相似文献
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利用扰动法导得了非线性强迫Boussinesq方程,利用数值解讨论了地形和外源等局地强迫激发的非线性长波扰动的一般性状和时间演变特征,并对移动性孤波与地形的相互作用进行了分析研究。 相似文献
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利用一种推广的代数方法,求解了一类广义Boussinesq方程(B(m,n)方程)和Boussinesq-Burgers方程(B-B方程).获得了其多种形式的显式精确解,包括孤波解、三角函数解、有理函数解、Jacobi椭圆函数周期解和Weierstrass椭圆函数周期解,进一步丰富了这两类方程的解.
关键词:
Boussinesq方程
Boussinesq-Burgers方程
推广的代数方法
显式精确解 相似文献
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利用Hirota方法及Riemann theta函数得到了(2+1)维Boussinesq方程的新的周期解.在极限情况下,该周期解退化为孤子解.
关键词:
Hirota方法
Riemann theta 函数
(2+1)维Boussinesq方程
周期解 相似文献
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采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解.
关键词:
齐次平衡法
孤子解
孤波解
广义Boussinesq方程
bidirectional Kaup-Kupershmi dt方程 相似文献
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Xi-zhong Liu 《中国物理 B》2022,31(5):50201-050201
A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method. To study various exact solutions of the nonlocal Boussinesq equation, it is converted into two local equations which contain the local Boussinesq equation. From the N-soliton solutions of the local Boussinesq equation, the N-soliton solutions of the nonlocal Boussinesq equation are obtained, among which the (N=2,3,4)-soliton solutions are analyzed with graphs. Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation. Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method. 相似文献
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Cheng Chen 《Waves in Random and Complex Media》2019,29(1):138-152
The generalized Kaup–Boussinesq equation is a model which is used to describe the water wave. In this paper, Lie group analysis method is used to perform detailed analysis on the generalized Kaup–Boussinesq equation. Some invariant solutions are obtained under the transformation groups. The conservation laws of the generalized Kaup–Boussinesq equation are constructed using two methods: multiplier method and Ibragimov theorem. 相似文献
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Jiefang Zhang Fengmin Wu Jianqing Shi 《International Journal of Theoretical Physics》2000,39(6):1697-1702
Malfliet first proposed a simple solution method for the multisoliton solutionofthe KdV equation. Abdel-Rahman used Malfliet's method in a slightly modifiedform, and gave the multisoliton solution of the mKdV equation, RLW equation,Boussinesq equation, and modified Boussinesq equation. In this paper, we solvethe soliton solution of the cKdV=nmKdV equation by using this method. 相似文献
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We study the stationary measure for the two-dimensional Boussinesq equation with random forcing. We prove the ergodicity for the two-dimensional stochastically forced Boussinesq equation. We also study the Galerkin truncations of the three-dimensional Boussinesq equations under degenerate stochastic forcing. We follow closely the previous results on the stochastically forced Navier–Stokes equations. 相似文献
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In the present study, we are concerned with the generalized Boussinesq equation including the singular sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. By using the extended auxiliary equation method, we obtained some new soliton like solutions for the two-dimensional sixth-order nonlinear Boussinesq equation with constant coefficients. These solutions include symmetrical, non-symmetrical kink solutions, solitary pattern solutions, Jacobi and Weierstrass elliptic function solutions and triangular function solutions. The stability analysis for these solutions is discussed. 相似文献
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The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painlevé analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves. 相似文献
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《Physica D: Nonlinear Phenomena》1986,21(1):171-176
A family of rational solutions of the Boussinesq equation is constructed. It provides examples of distinct rational solutions of the Boussinesq equation which have the same function as limit when t goes to zero. 相似文献
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A Variational Iteration Solving Method for a Class of Generalized Boussinesq Equations 总被引:2,自引:0,他引:2
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We study a generalized nonlinear Boussinesq equation by introducing a proper functional and constructing the variational iteration sequence with suitable initial approximation. The approximate solution is obtained for the solitary wave of the Boussinesq equation with the variational iteration method. 相似文献