Author:
Abdoulkary Saïdou,Mohamadou Alidou
Abstract
We consider the nonlinear Schrödinger equation modified by a rational nonlinear term. The model appears in various studies often in the context of the Ginzburg-Landau equation. We investigate modulational instability by means of a linear stability analysis and show how the nonlinear terms affect the growth rate. This analytical result is confirmed by a numerical simulation. The latter analysis shows that breather-like solitons are generated from the instability, and the effects of the nonlinear terms are again clearly seen. Moreover, by employing an auxiliary-equation method we obtain kink and anti-kink soliton as analytical solutions. Our theoretical solution is in good agreement with our numerical investigation.
Reference15 articles.
1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, California, 2001).
2. B. A. Malomed, L. Stenflo, J Phys A: Math Gen 24 L1149 (1991).
3. E. Yomba, T. C. Kofane, Chaos, Solitons and Fractals 17 847 (2003).
4. A. Mohamadou et al. Chaos, Solitons and Fractals 27 914–925 (2006).
5. V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Soy. Phys. JETP 34, 62 (1972)].