导数非线性Schrödinger方程的孤子解和流氓波解-第2部分

Guo-quan Zhou
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引用次数: 0

摘要

通过在Zakharov-Shabat IST积分中引入合适的仿射参数,提出了具有恒定非消失边界条件(NVBC)和正群速度色散的DNLS+方程的修正和严格证明的逆散射变换(IST);利用代数方法导出了显式呼吸型解和纯n孤子解。另一方面,以谐波平面波为不消失背景的DNLS方程也采用Hirota的双线性形式进行求解。确定了它的空间周期解,并导出了它的异动波解作为该空间周期解的长波极限。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Soliton and Rogue-Wave Solutions of Derivative Nonlinear Schrödinger Equation - Part 2
A revised and rigorously proved inverse scattering transform (IST for brevity) for DNLS+ equation, with a constant nonvanishing boundary condition (NVBC) and normal group velocity dispersion, is proposed by introducing a suitable affine parameter in the Zakharov-Shabat IST integral; the explicit breather-type and pure N-soliton solutions had been derived by some algebra techniques. On the other hand, DNLS equation with a non-vanishing background of harmonic plane wave is also solved by means of Hirota’s bilinear formalism. Its space periodic solutions are determined, and its rogue wave solution is derived as a long-wave limit of this space periodic solution.
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