The general Klein–Gordon–Schrödinger system: modulational instability and exact solutions
The general Klein–Gordon–Schrödinger system: modulational instability and exact solutions
复制标题
一般克莱因-戈登-薛定谔系统：调制不稳定性和精确解
DOI：
10.1088/0031-8949/77/01/015004
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Wei Ding
中科院分区：
文献类型：
--
作者：
Xiaoyan Tang;Wei Ding
研究了在非线性薛定谔场和非线性Klein-Gordon场中都引入立方自相互作用的一般Klein-Gordon-Schrödinger（gKGS）系统.我们首先研究了系统的调制不稳定性（MI），并由此导出了调制扰动的频率和波数之间的一般色散关系，从而证明了MI区域的多种可能性。使用行波减少，gKGS系统大大简化。通过一种简单的函数展开方法，我们得到了一些精确的行波解。在特定的参数下，图形显示了一些典型的波结构，包括扭结、反扭结、亮孤子、暗孤子、灰孤子和周期孤子。
The general Klein–Gordon–Schrödinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schrödinger and the nonlinear Klein–Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons.