Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations

Abstract

We consider the inhomogeneous (1+1)-dimensional coupled nonlinear Schrödinger equations from the integrability point of view. This system has potential applications in inhomogeneous birefringent fiber media or in optical communication links with variable parameters. The exact analytical multisoliton solutions are obtained by employing the simple, straightforward Darboux transformation based on the obtained 3 × 3 Lax pair. Some main propagation and interaction properties of the one- and two-soliton solutions are discussed simultaneously. Also, the interaction between two neighboring combined solitary waves is numerically discussed. Excellent agreement with analytical results are found in the case of no collision. Moreover, the stability of these solutions are discussed in detail numerically with respect to a finite perturbation.

Keywords:

• inhomogeneous nonlinear Schrödinger equation
• Darboux transformation
• soliton solutions
• Lax pair

Acknowledgements

KP wishes to thank the IFCPAR (No. IFC/3504- F/2005/2064), CSIR, DST-DFG and DST Ramanna Fellowship, Government of India, for financial support through major projects.