Engineering nonautonomous chirped rogue waves in coupled nonlinear Schr?dinger equations with external potentials in normal dispersion regimes

A coupled cubic nonlinear Schrodinger (NLS) equations with external potentials in normal dispersion regimes is considered. Combining the phase engineering technique with a modified lens transformation, the integrability condition is derived and the equations are reduced to an integrable Kundu-Eckhaus (KE) equation that always admits rogue wave solutions and can be used to model the propagation of femtosecond pulses in nonlinear and quantum optics. Exploiting known rogue wave solutions of the derived KE equation, we build exact first-order breather and rogue wave and second-order rogue wave solutions with nonlinear frequency chirping of the NLS equation under consideration; these exact solutions contain a number of parameters (solution parameters). For two types of Kerr nonlinearity, namely the periodically and kink-like modulated nonlinearities, we engineer nonautonomous chirped rogue waves in nonlinear systems governed by the coupled nonlinear Schrodinger equations under consideration. The properties of the found nonautonomous rogue waves and the corresponding chirp are investigated. Our results show that the frequency chirp saturates at some finite value as the retarded time approaches its asymptotic value. The effects of various solution parameters on the dynamics of found nonlinear waves are also investigated. Interestingly, we show that modulating some solution parameters results in a significant rotation of the first-and second-order rogue waves in the clockwise direction.