NEW TYPES OF INTERACTIONS BASED ON VARIABLE SEPARATION SOLUTIONS VIA THE GENERAL PROJECTIVE RICCATI EQUATION METHOD
NEW TYPES OF INTERACTIONS BASED ON VARIABLE SEPARATION SOLUTIONS VIA THE GENERAL PROJECTIVE RICCATI EQUATION METHOD
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DOI：
10.1142/s0129055x07002948
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发表时间：
2007-03
影响因子：
1.8
通讯作者：
C. Dai;Jie-Fang Zhang
中科院分区：
文献类型：
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作者：
C. Dai;Jie-Fang Zhang
本文首先应用广义投影Riccati方程方法（PREM）导出（2 + 1）维系统的分离变量解。通过进一步的研究，我们发现PREM得到的这些分离变量解，看似独立，实际上是相互依赖的。本文给出了（2 + 1）维广义Nizhnik-Novikov-Veselov系统、Broer-Kaup-Kupershirt方程、色散长波系统、Boiti-Leon-Pempinelli模型、广义Burgers模型、广义Ablowitz-Kaup-Newell-Segur系统和Maccari方程等物理量的一个通用公式。本文将唐、娄、张[2]中的普适公式简化为一般公式。其次，将该方法成功地推广到（1 + 1）维系统，如耦合的可积无色散方程、浅水波方程、Boiti系统和负KdV模型，并得到了描述这些（1 + 1）维模型的合适物理场或势的另一个通用公式，该公式与（2 + 1）维系统中的公式类似。最后，基于（2 + 1）维系统的通用公式，通过选取适当的多值函数，研究了特殊dromion、特殊peakon、foldon和semifoldon之间的弹性和非弹性相互作用。此外，给出了由通用公式提供的所有局域激发的显式相移，并将其应用于这些新的相互作用中。
In this paper, first, the general projective Riccati equation method (PREM) is applied to derive variable separation solutions of (2 + 1)-dimensional systems. By further studying, we find that these variable separation solutions obtained by PREM, which seem independent, actually depend on each other. A common formula with some arbitrary functions is obtained to describe suitable physical quantities for some (2 + 1)-dimensional models such as the generalized Nizhnik–Novikov–Veselov system, Broer–Kaup–Kupershmidt equation, dispersive long wave system, Boiti–Leon–Pempinelli model, generalized Burgers model, generalized Ablowitz–Kaup–Newell–Segur system and Maccari equation. The universal formula in Tang, Lou, and Zhang [2] can be simplified to the common formula in the present paper. Second, this method is successfully generalized to (1 + 1)-dimensional systems, such as coupled integrable dispersionless equations, shallow water wave equation, Boiti system and negative KdV model, and is able to obtain another common formula to describe suitable physical fields or potentials of these (1 + 1)-dimensional models, which is similar to the one in (2 + 1)-dimensional systems. Finally, based on the common formula for (2 + 1)-dimensional systems and by selecting appropriate multivalued functions, elastic and inelastic interactions among special dromion, special peakon, foldon and semi-foldon are investigated. Furthermore, the explicit phase shifts for all the local excitations offered by the common formula have been given, and are applied to these novel interactions in detail.