Localized Coherent Structures of the(2+1)-Dimensional Higher Order Broer-Kaup Equations
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摘要: 利用推广的齐次平衡方法,研究高阶(2+1)维Broer-Kaup方程的局域相干结构.首先基于推广的齐次平衡方法,给出这个模型的一个非线性变换,并把它变换成一个线性化的方程.然后从线性化方程出发,构造出一个分离变量的拟解.由于拟解中不仅含有两个y的任意函数,而且还有{αi,βi,γk,kj,lk}和{N,M,L}这些参数可以任意选取,因此合适的选择这些函数和参数,可以得到新的相当丰富的孤子结构.方法直接而简单,可推广应用一大类(2+1)维非线性物理模.
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关键词:
- 扩展齐次平衡法 /
- 高阶Broer-Kaup方程 /
- (2+1)维 /
- 孤子解 /
- dromion解
Abstract: By using the extended homogeneous balance method,the localized cohernet structures are studied.A nonlinear transformation was first established,and then the linearization form was obtained based on the extended homogeneous balance method for the higher order(2+1)-dimensional Broer-Kaup equations.Starting from this linearization form equation,a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed.The quite rich localized coherent structures were revealed.This method,which can be generalized to other(2+1)-dimensional nonlinear evolution equation,is simple and powerful. -
[1] Boiti M,Leon J J P,Martina L,et al.Scattering of localized solitons in the plane[J].Phys Lett A,1988,132(8-9):432-439. [2] Fokas A S,Santini P M.On the simplest integrable equation in 2+1[J].Phyisica D,1990,44(1):99-104;Hietarinta J,Hirota R.Multidromion solutions to the Davey-Stewartson equation[J].Phys Lett A,1990,145(5):237-244. [3] Hietarinta J.One-dromion solutions for generic classes of equations[J].Phys Lett A,1990,149(2-3):113-117. [4] Radha R,Lakshmanan M.Singularity analysis and localized cohernet structures in(2+1)-dimensional generalized Korteweg-de Vries equations[J].J Math Phys,1994,35(9):4746-4756. [5] Radha R,Lakshmanan M.Dromion like structures in the(2+1)-dimensional breaking soliton equation[J].Phys Lett A,1995,197(1):7-12. [6] Radha R,Lakshmanan M.Exotic coherent structures in the(2+1)-dimensional long dispersive wave equation[J].J Math Phys,1997,38(2):292-299. [7] Radha R,Lakshmanan M.A new class of induced localized structures in the(2+1)-dimensional scalar nonlinear Schrdinger equations[J].J Phys A,1997,30:3229-3232. [8] Lou S Y,Dromion-like structures in a(3+1)-dimensional KdV-type equation[J].J Phys A,1996,29:5989-6001. [9] Ruan H Y,Lou S Y.Higher-dimensional dromion structures:Jimbo-Miwa-Kadomtsev-Petviashvili system[J].J Math Phys,1997,38(6):3123-3136. [10] Lou S Y.Generalized dromion solutions of the(2+1)-dimensional KdV equation[J].J Phys A,1995,28:7227-2732. [11] Lou S Y.On the dromion solutions of the potential breaking soliton equation[J].Commun Theor,1996,26(4):487-492. [12] Radha R,Lakshmanan M.Generalized dromions in the(2+1)-dimensional long dispersive wave(2LDW) and scalar nonlinear Schrdinger(NLS) equations[J].Chaos Solitons & Fractals,1999,10:1821-1824. [13] ZHANG Jie-fang.Generalized dromions of the(2+1)-dimensional nonlinear Schrdinger equations[J].Communcation in Nonlinear Science & Numerical Simulation,2001,6(1):50-53. [14] ZHANG Jie-fang.A simple soliton solution method for the(2+1)-dimensional long dispersive wave equations[J].Acta Physica Sinica(Overseas Edition),1999,8(2):326-330. [15] Lou S Y.On the coherent structures of the Nizhnik-Novikov-Veselov equation[J].Phys Lett A,2000,277:94-100. [16] Lou S Y,Ruan H Y.Revisitation of the localized excitations of the(2+1)-dimensional KdV equation[J].J Phys A:Math Gen,2001,34:305-316. [17] RUAN Hang-yu,CHEN Yi-xin.Ring solitions,dromions,breathers and instantons of the NLS equation[J].Acta Physica Sinica,2001,50(4):586-591. [18] WANG Ming-liang.The solitary wave solutions for variant Boussinesq equations[J].Phys Lett A,1995,199:169-172. [19] ZHANG Jie-fang.Multiple solitions of long liquid wave equations[J].Acta Physica Sinica,1999,47(9):1416-1420;Multi-soliton solutions of the dispersive long wave equation[J].Chin Phys Lett,1999,16(1):659-661. [20] ZHANG Jie-fang.Bcklund transformation and multisoliton-like solution of the(2+1)-dimensional dispersive long wave equations[J].Commun Theor Phys,2000,33(4):577-582. [21] FANG Een-gui,ZHANG Hong-qing.Solitary wave solution of nonlinear wave equqtion[J].Acta Physica Sinica,1997,46(1):1254-1259. [22] LOU Sen-yue,WU Xing-biao.Broer-Kaup systems from Darboux transformation related symmetry constraints of KP equation[J].Commun Theor Phys,1998,29(1):145-148.
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