مشخصات پژوهش

In this paper, we investigate the traveling soliton and the per iodic wave solutions of the nonlinear Schr€ odinger equation (NLSE) wit h generalized nonlinear function ality. We also explore the underlyin g close connection between the well-known KdV equation and the NLSE . It is remarked that bot h one-dimension al KdV and NLSE mo dels shar e the same pseudoen ergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlin ear mathematical models, namely, the Helmholt z and the Du ffing oscillators’ pot entials. It is fo und that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequ ency ratio for the Helmholtz potential between the nonlinear per iodic carrier and the modulated sinusoida l waves is always in the range 0.5  X/x  0.537285 regardless of the potential parameter values. The values of X/x ¼ {0.5, 0.537285} correspond to the cnoidal waves modulus of m ¼ {0, 1} for soliton and sinusoidal limits and m ¼ 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.