Soliton solutions of the Sasa-Satsuma equation in the monomode optical fibers including the beta-derivatives

A coupled space-time fractional nonlinear Schrodinger equation is solved by the fractional Riccati method and fractional dual-function method. By choosing the appropriate values of parameters, we obtain exact analytical vector soliton and periodic solutions constructed by the Mittag–Leffler function and give the special conditions for the formation of solitons. The two- and three-dimensional graphs of these solutions are displayed. These solutions are helpful to understand the complex physical and engineering problems described by the coupled space-time fractional nonlinear Schrodinger equation.

Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrödinger equation

This paper analytically explores a (2 + 1)-dimensional nonlinear model with the beta time derivative describing the wave propagation in the Heisenberg ferromagnetic spin chain. Particularly, after allocating the beta time derivative to the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain (2D-HFSC) model, its 1-soliton solutions are formally derived through utilizing a group of systematic techniques such as the new Kudryashov and exponential methods. Some graphical representations in three-dimensional postures are considered to analyze the impact of the beta parameter on the dynamical behavior of the bright and dark solitons.

1-Soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative

The main goal of this paper is to discover some new analytical solutions of a fractional form of the Bogoyavlensky–Konopelchenko equation via two new analytical schemes. This model is considered as a particular case of (2 + 1)–dimensional version of the well–known KdV equation where it describes the interaction between the Riemann wave propagating and the long-wave propagation along the x , y –axises. An efficient fractional derivative called Atangana–Baleanu-Riemann derivative is utilized to convert the standard form of the model into a nonlinear fractional PDE with an–integer order. The basic idea in these methods is to use a new variable to transform the form of the equation into a nonlinear equation with ordinary derivatives. The novelty of the present paper is that the new solutions determined by applying these two powerful analytical methods can not be found in previous articles. Several two and three-dimensional figures have been depicted to illustrate the dynamic behavior of the acquired solutions. Another advantage of these two methods is their applicability in solving similar models using this fractional derivative operator.

Novel exact solutions of the fractional Bogoyavlensky–Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative

The nonlinear Schrodinger equation (NLSE) in (2 + 1) dimensions with beta derivative evolution is considered here to study nonlinear coherent structures for Heisenberg models of ferromagnetic spin ...

Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness

In this paper, the conformable sub-equation method is proposed to construct exact solutions of the space-time resonant nonlinear Schrodinger equation (R-NLSE). Conformable derivatives are described...

J. F. Gómez-Aguilar

Papers

Optical solitons solution of resonance nonlinear Schrödinger type equation with Atangana's-conformable derivative using sub-equation method