中国物理B ›› 1994, Vol. 3 ›› Issue (1): 1-17.doi: 10.1088/1004-423X/3/1/001

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GENERAL SOLITON SOLUTIONS OF THE NLS+ EQUATION UNDER NON-VANISHING BOUNDARY CONDITION

陈宗蕴1, 黄念宁2, 李再光3   

  1. (1)Department of Physics, and National Laboratory of Laser Technology, Huazhong University of Sicience and Technology, Wuhan 430074, China; (2)Department of Physics, Wuhan University, Wuhan 430072, China; Institute of Theoretical Physics, Academia Sinica, Beijing 100080, China; (3)National Laboratory of Laser Technology, Huazhong University of Science and Technology, Wuhan 430074, China
  • 收稿日期:1993-04-26 出版日期:1994-01-20 发布日期:1994-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China and the Chinese National Fund for Nonlinear Science Research.

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   

  1. 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
  • Received:1993-04-26 Online:1994-01-20 Published:1994-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China and the Chinese National Fund for Nonlinear Science Research.

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摘要： 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.

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.

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Zz (Inverse problems)