New Solutions for Chirped Optical Solitons Related to Kaup-Newell Equation: Application to Plasma Physics

In this work, some new periodic and localized analytical solutions in the framework of the Kaup-Newell equation (KNE) which is considered one of the most popular forms of the derivative nonlinear Schrödinger equation (DNLSE) are constructed. The evolution equation is reduced to a cubic-quintic Duffing equation (CQDE) using traveling wave transform for describing the dynamics of nonlinear structures that can exist and propagate in nonlinear and dispersive media (e.g. optical fiber and plasma physics). The CQDE is solved in terms of the Jacobian elliptic functions; cn, sn, sc, F, and Π and a general solution in the form of cnoidal waves is obtained. Here, the solution of CQDE is solved based on the Jacobian elliptic functions theory. The obtained solutions are in the form of elliptic periodic, chirped solitons, and trigonometric. These solutions are generalized as compared to other published solutions. Also, the chirped soliton solution can be derived directly from the cnoidal solution as a special case. The model is applied to the description of the propagation of modulated structures in optical fiber and in plasma physics especially Alfvén waves.