(2+1)维广义Borer-Kaup系统的变量分离解和半包局域结构  

VARIABLE SEPARATION SOLUTIONS AND SEMIFOLDED LOCALIZED STRUCTURES FOR(2+1)-DIMENSIONAL GENERALIZED BORER-KAUP SYSTEM

作　　者：叶健芬[1] 郑春龙[2] 陈立群[2] 

机构地区：[1]浙江丽水学院物理系 [2]上海大学应用数学和力学研究所,上海200072

出　　处：《动力学与控制学报》2005年第4期24-29,共6页Journal of Dynamics and Control

基　　金：浙江省自然科学基金(Y604106);浙江省"新世纪151人才工程"基金;浙江省重点学科科研基金资助项目~~

摘　　要：基于一个特殊的Painlev啨Bcklund变换和多线性变量分离方法,分析了(2+1)维非线性广义BorerKaup(GBK)系统,求得了该系统具有若干任意函数的变量分离严格解.根据得到的变量分离严格解,并通过选择解中的任意函数,引入恰当的局域函数和多值函数,找到了GBK系统一种新的具有实际物理意义的半包局域相干结构,如海洋表面波,并简要地讨论了这种半包局域相干结构的一些特殊的演化性质.结果表明:这种半包局域相干结构相互作用后,完全保持它们原有的速度、波形和波幅,即它们的演化性质是完全弹性的.Starting from a special Painlevé-Baecklund transformation and a multilinear variable separation approach, the （2 ＋ 1 ）-dimensional generalized Borer-Kaup（GBK） system was analyzed, and a general variable separation excitation with rome arbitrary functions for the （2 ＋ 1 ）-dimensional GBK system was derived. Based on the derived variable separation excitation and by selecting the arbitrary functions in the exact ,solution appropriately, such as certain localized functions and multi-valued functions, a new type of solitary wave, i.e. , a semifolded localized structure with practical meaning like ocean surface waves for the GBK system was constructed, and its evolution property of the novel localized structures was briefly discussed. The results show that it is completely elastic interaction, because the semifolded localized coherent structures are completely preserved, and their initial velocities, wave shapes and amplitudes are preserved after collision.

关 键 词：广义Borer-Kaup系统 多线性变量分离法 半包局域结构 

分 类 号：O411.1[理学—理论物理]