Rogue Wave Solutions Of A Higher Order Chen-Lee-Liu Equation

The Chen-Lee-Liu equation was introduced as an integrable model in 1979. In 2007, an experiment testified in optical pulses propagation involving self-steepening without selr-phase-modulation. This experiment provides the physical meaning of the Chen-Lee-Liu equation. We consider a next-higher-order extension of the Chen-Lee-Liu equation, i.e., a higher-order Chen-Lee-Liu (HOCLL) equation with third order dispersion and quintic nonlinearity terms. We construct the n-fold Darboux transformation (DT) of the HOCLL equation in terms of the n x n determinants. Comparing with the nonlinear Schrodinger equation, the derivation of the determinant representation Tn for HOCLL is involved with the complicated integrals although we eliminate these integrals in the final form of DT, so that the DT of the HOCLL equation is unusual. We provide the explicit expressions of multi-rogue wave solutions for the HOCLL equation. It is concluded that the rogue wave solutions are likely to be a crucial model to consider the higher-order nonlinear effects.