GENERAL SOLITON SOLUTIONS OF THE NLS+ EQUATION UNDER NON-VANISHING BOUNDARY CONDITION
CHEN ZONG-YUN (陈宗蕴)a, LI ZAI-GUANG (李再光)b, HUANG NIAN-NING (黄念宁)c
a Department of Physics, and National Laboratory of Laser Technology, Huazhong University of Sicience and Technology, Wuhan 430074, China; b National Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 430074, China; c Department of Physics, Wuhan University, Wuhan 430072, China; Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China
Abstract For the NLS+ equation under nonvanishing boundary condition, to avoid complexity due to Riemann surface, required for double-valued function of the usual spectral parameter, starting from a particular auxiliary spectral parameter, a special inverse scattering method is systematically developed, and explicit expressions of the general multi-soliton solutions are successfully obtained. Asymptotic behaviors of the muiti-soliton solutions, additional displacement of center and additional phase shift of the peak are derived. When the boundary value approaches zero, all the formulas become the known ones naturally.
Received: 26 April 1993
Accepted manuscript online:
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