We consider a derivative nonlinear Schrödinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the nonlinearity and, in some instances, their velocity. We illustrate these results with numerical simulations.

We see how we can improve the accessibility of Newton’s method for approximating a solution of a nonlinear equation in Banach spaces when a center Hölder condition on the first derivative is used to prove its semi-local convergence.

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.

The aim of this paper is to present the relationship between the classical linearization and the optimal derivative of a nonlinear ordinary differential equation. An application is presented using the quadratic error. AMS subject classification: 34A30, 34A34.

We consider a derivative nonlinear Schrödinger equation with general nonlinearlity: $$\begin{aligned} i\partial _tu+\partial _x^2u+i|u|^{2\sigma }\partial _xu=0, \end{aligned}$$ In Tang and Xu (J Differ Equ 264(6):4094–4135, 2018), the authors prove stability of two solitary waves in energy space for $$\sigma \in (1,2)$$ . As consequence, there exists solution above which is close arbitrary to ...

This article consists of Improved Bernoulli Sub-Equation Function Method (IBSEFM) to get the new solutions nonlinear fractional Schrödinger equation described by beta-derivative. Foremost, it is dealt with derivative Atangana. Secondly, basic properties IBSEFM are given. Finally, proposed method has been applicated considered its solutions. Moreover, graphs obtained plotted via Mathematica. It ...