Soliton interaction under the influence of higher-order effects

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 Schr€ odinger (HNLS) equation. As examples, oneand 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 higherorder effects can restrain the interaction between neighboring solitons to some extent. The results are proved by directly solving HNLS equation numerically. 2002 Elsevier Science B.V. All rights reserved. PACS: 42.81.Dp; 42.65.R; 42.65.W