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白成林  刘希强  赵红 《中国物理》2005,14(2):285-292
Starting with the extended homogeneous balance method and a variable separation approach, a general variable separation solution of the Broer—Kaup system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakon and fractal localized solutions, some new types of localized excitations, such as compacton and folded excitations, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple-valued functions, and some interesting novel features of these structures are revealed.  相似文献   
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高阶Broer-Kaup(BK)方程组的新精确解   总被引:1,自引:1,他引:0  
利用扩展齐次平衡法,我们得到了1+1维和2+1维高阶BK方程组新的孤子解和无穷多有理函数解,尤其是求出了初始值问题解的封闭形式.  相似文献   
3.
马正义  朱加民  郑春龙 《中国物理》2004,13(9):1382-1385
This work reveals a novel phenomenon—that the localized coherent structures of a (2﹢1)﹣dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2﹢1)﹣dimensional higher-order Broer-Kaup system as a concrete example. Starting from a B?cklund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.  相似文献   
4.
A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-order Broer-Kaup equation by means of WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are found to be completely elastic.  相似文献   
5.
Under investigation in this paper, with symbolic computation, is the Whitham–Broer–Kaup (WBK) system for the dispersive long waves in the shallow water small-amplitude regime. N-fold Darboux transformation (DT) for a spectral problem associated with the WBK system is constructed. Odd-soliton solutions in terms of the Vandermonde-like determinant for the WBK system are presented via the N-fold DT and evolution of the three-soliton solutions is graphically studied. Our results could be used to illustrate the bidirectional propagation of the waves in the shallow water small-amplitude regime.  相似文献   
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(2+1)维Broer-Kaup方程的局域相干结构   总被引:21,自引:1,他引:20       下载免费PDF全文
张解放  韩平 《物理学报》2002,51(4):705-711
利用推广的齐次平衡方法,研究了(2+1)维BroerKaup方程的局域相干结构.首先根据领头项分析,给出了这个模型的一个变换,并把它变换成一个线性化的方程,然后由具有两个任意函数的种子解构造出它的一个精确解,发现(2+1)维BroerKaup方程存在相当丰富的局域相干结构.合适的选择这些任意函数,一些特殊型的多dromion解,多lump解,振荡型dromion解,圆锥曲线孤子解,运动和静止呼吸子解和似瞬子解被得到.孤子解不仅可以存在于直线孤子的交叉点上,也可以存在于曲线孤子的交叉点或最临近点上.呼吸子在幅度和形状上都进行了呼吸.本方法直接而简单,可推广应用一大类(2+1)维非线性物理模型. 关键词: 浙江师范大学非线性物理研究室 金华321004 浙江海洋学院物理系 舟山316004  相似文献   
8.
Painleve property of the (2+1)-dimensional multi-component Broer-Kaup (BK) system is considered by using the standard Weiss Kruskal approaches. Applying the Clarkson and Kruskal (CK) direct method to the (2+1)- dimensional multi-component BK system, some types of similarity reductions are obtained. By solving the reductions, one can get the solutions of the (2+1)-dimensional multi-component BK system.  相似文献   
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