Construction solitons for fractional nonlinear Schrödinger equation with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg"> <mml:mi>β</mml:mi> </mml:math> -time derivative by the new sub-equation method

Abstract

This article applies the new sub-equation method to derive soliton solutions and other solutions for unstable and modified unstable nonlinear Schrödinger equations with β-time derivative. Dark solitons, bright-singular combo solitons and singular solitons are obtained. Also, periodic solutions, rational solutions and exponential solutions are reported. After giving suitable values to parameters, the novel structures of solutions are depicted. The physical surfaces of some gained solutions in different forms are shown graphically, which helpful for understanding the complex physical phenomena of these dynamical models. The results show the superiority of executed method, which is applicable to many other nonlinear physical equations.