Dynamics of large-amplitude solitons
Dynamics of large-amplitude solitons
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DOI：
10.1134/1.558966
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发表时间：
1999-07
影响因子：
1.1
通讯作者：
A. Slyunyaev;E. Pelinovski
中科院分区：
文献类型：
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作者：
A. Slyunyaev;E. Pelinovski
考虑了允许极限幅值孤子存在的非线性可积系统中孤子的相互作用和产生问题。考虑的可积系统是Gardner方程，它包括Korteweg-de Vries方程（二次非线性）和修正的Korteweg-de Vries方程（三次非线性）作为特殊情况。导出了Gardner方程的双孤子解，并确定了区分两个孤子相互作用不同情形的判据。考虑了初始脉冲扰动的演化过程。特别指出，在这种演化过程中，在极限孤子的波峰上出现极性相反的孤子。
The interaction and generation of solitons in nonlinear integrable systems which allow the existence of a soliton of limiting amplitude are considered. The integrable system considered is the Gardner equation, which includes the Korteweg-de Vries equation (for quadratic nonlinearity) and the modified Korteweg-de Vries equation (for cubic nonlinearity) as special cases. A two-soliton solution of the Gardner equation is derived, and a criterion, which distinguishes between different scenarios for the interaction of two solitons, is determined. The evolution of an initial pulsed disturbance is considered. It is shown, in particular, that solitons of opposite polarity appear during such evolution on the crest of a limiting soliton.