Affiliation: | a Department of Electronics and Information Technology, Shanxi University, Taiyuan 030006, China b The State Key, Subjects of Optics, Shanxi University, Taiyuan 030006, China c Department of Physics and Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, China |
Abstract: | In this paper, we present exact N-soliton solution by employing simple, straightforward Darboux transformation based on the Lax pair for Hirota equation, a higher-order nonlinear Schrödinger (HNLS) equation. As examples, one- and two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one can adjust frequency shift for each soliton appropriately. Further, we obtain the approximate eigenvalues by employing two-soliton solution and discuss analytically the interaction between neighboring solitons under the influence of the higher-order effects. It is shown that the combined effects of the higher-order effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically. |