Abstract
In this study, the (2+1)-dimensional cubic nonlinear Schrödinger equation with fractional temporal evolution is investigated by using the extended sinh-Gordon equation expansion method. The idea of conformable fractional derivative is used in transforming the complex nonlinear partial differential equation to nonlinear ordinary differential equation. Dark, bright, mixed dark-bright, singular, mixed singular solitons and singular periodic wave solutions are successfully reached. The parametric conditions for the existence of valid solitons are given. The 2D and 3D graphics to some of the reported solutions are plotted.
Highlights
Nonlinear Shrodinger’s type equations (NLSEs) are special kind of nonlinear evolution equations expressing several complex nonlinear aspect in the field of nonlinear sciences such as the optical fiber, fluid mechanics, plasma physics, biology, hydrodynamics and so on
Several analytical techniques have been used to find the solutions of various NLSEs [1,2,3,4,5,6,7,8,9,10,11,12]
By the extended sinh-Gordon equation expansion method (ShGEEM), the solutions of any given nonlinear partial differential equation are assumed to be of the forms [14]
Summary
Nonlinear Shrodinger’s type equations (NLSEs) are special kind of nonlinear evolution equations expressing several complex nonlinear aspect in the field of nonlinear sciences such as the optical fiber, fluid mechanics, plasma physics, biology, hydrodynamics and so on. The (2+1)-dimensional cubic nonlinear Schrödinger equation with fractional temporal evolution [13] is going to be soughted by using the extended sinh-Gordon equation expansion method (ShGEEM) [14,15,16,17]. The (2+1)-dimensional cubic nonlinear Schrödinger equation with fractional temporal evolution is given by [13]. When 1, we have the original (2+1)-dimensional cubic nonlinear Schrödinger equation [13]
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