Dynamics of self-reinforcing matter-wave in gravito-optical surface trap

Abstract

We consider matter-wave solitons/oscillons in the presence of gravito-optical surface traps within the framework of mean-field equations. We pay special attention to the dynamics of both solitons and oscillons against the reflecting platform, the position of which can either be varied periodically or quasiperiodically with time. It is seen that with the temporal variation of reflector’s vertical position, the dynamics of the soliton can change from periodic to quasiperiodic while that of the oscillon can change from regular to chaotic. We find that the transition from regular to chaotic motion is prominent in Poincaré maps for different relevant recurrence times.

The influence of the differential conformable operators through modern exact solutions of the double Schrödinger-Boussinesq system

“…Remark 4.1. It is well recognized that the solitary waves have an evident role in the different nonlinear physical phenomena, like self-reinforcing systems, nuclear physics, optical fibers, plasma physics, and so on [49,[51][52][53]. In our present work, the exact solutions (24)-(47) of the system (1) can be turned into solitary wave solutions via the identity…”

“…Moreover, the exact solutions that emerged by the KM are wave solutions of solitary and periodic types which have evident roles in many disciplines [47][48][49]. In the following section, we apply the KM for constructing new solitary and periodic solutions for the system (1).…”

Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

“…It is recognized that the broadly applied types of traveling wave solutions are the soliton and periodic wave solutions. Soliton wave solutions have a major role in various physical scopes, such as optical fibers, plasma physics, self-reinforcing systems, nuclear physics, and others [38][39][40][41]. Furthermore, periodic wave solutions have an apparent role in different physical phenomena, as in diffusion-advection systems, collisionless plasmas, impulsive systems, and so on [42][43][44].…”

“…The acquired stochastic solutions ( 33)- (39) of Equation ( 14) can be readily converted to stochastic solutions of the soliton wave type via the identity exp (O) = cosh (O) + sinh (O). For instance, the solution U 1 (p, q) can be turned into the following stochastic wave solution of the soliton type:…”

“…and Ω(p, q) is defined by Equation (35). Furthermore, from the identity exp (iO) = cos (O) + i sin (O), the acquired stochastic solutions (33)- (39) of Equation ( 14) can be easily converted to stochastic solutions of the periodic wave type. In particular, the solution U 1 (p, q) can be be turned into the following stochastic wave solution of the periodic type:…”