Abstract
AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.
Highlights
This paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme
This paper addresses optical Gaussons using the Laplace–Adomian decomposition method (LADM)
In the present case, the optical Gaussons solution of the nonlinear Schrödinger’s equation (NLSE) with log-law nonlinearity is given by u (x, t) = Ae−B2 (x−νt)2ei [−κx+ωt+θ]
Summary
To study the behavior of Gaussons, we consider the dimensionless form of the NLSE with log-law nonlinearity considered in ref. [19,20,21] and given by. In the present case, the optical Gaussons solution of the NLSE with log-law nonlinearity is given by u (x, t) = Ae−B2 (x−νt)2ei [−κx+ωt+θ]. Solving for Ltu(x, t) and applying Laplace transform on both sides of equation (13), we obtain In this case, the starting hypothesis for log-law nonlinearity is given by [4,22,26]. Considering the initial condition given in equation (13), u(x, t) are obtained by applying the inverse Laplace transform −1 on both sides of equation (16) The convergence of this series has been studied in ref. The Laplace transform decomposition algorithm given by equation (22) is applied to find the solution to the following NLSE with log-law nonlinearity (1): ut (x, t) = iauxx (x, t) − if (x)u (x, t) + ibu (x, t)ln |u (x, t)|2.
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