Integration of the soliton hierarchy with self-consistent sources
Integration of the soliton hierarchy with self-consistent sources
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DOI：
10.1063/1.533420
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发表时间：
2000-07
影响因子：
1.3
通讯作者：
Yunbo Zeng;W. Ma;Runliang Lin
中科院分区：
文献类型：
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作者：
Yunbo Zeng;W. Ma;Runliang Lin
与孤立子方程相比，具有自洽源的孤立子方程（SESCS）的Lax表示中本征函数的演化具有奇异性。我们提出了一个通用的方法来处理奇异性，以确定散射数据的演变。利用逆散射方法直接积分了自洽源AKNS方程族、自洽源MKdV方程族、自洽源非线性Schrodinger方程族、自洽源Kaup-Newell方程族和自洽源导数非线性Schrodinger方程族。给出了某些SESCS的N孤子解。结果表明，源的插入会引起孤子速度的变化。这种方法可以应用到所有其他的（1+1）维孤子族。
In contrast with the soliton equations, the evolution of the eigenfunctions in the Lax representation of soliton equation with self-consistent sources (SESCS) possesses singularity. We present a general method to treat the singularity to determine the evolution of scattering data. The AKNS hierarchy with self-consistent sources, the MKdV hierarchy with self-consistent sources, the nonlinear Schrodinger equation hierarchy with self-consistent sources, the Kaup–Newell hierarchy with self-consistent sources and the derivative nonlinear Schrodinger equation hierarchy with self-consistent sources are integrated directly by using the inverse scattering method. The N soliton solutions for some SESCS are presented. It is shown that the insertion of a source may cause the variation of the velocity of soliton. This approach can be applied to all other (1+1)-dimensional soliton hierarchies.