The Fokas--Lenells (FL) equation arises as a model equation which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order [in the leading asymptotic order the nonlinear Schrödinger (NLS) equation results]. Here we present an explicit analytical representation for the rogue waves of the FL equation. This representation is constructed by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution. When certain higher-order nonlinear effects are considered, the propagation of rogue waves in optical fibers is given.
Journal of the Physical Society of Japan
- Pub Date:
- December 2012
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- Mathematics - Analysis of PDEs
- 7 pages, 3 figures