Rouge Wave, W-Shaped, Bright, and Dark Soliton Solutions for a Generalized Quasi-1D Bose–Einstein Condensate System with Local M-Derivative

Abstract

In this paper, a generalized quasi-1D Bose-Einstein condensate system with contact repulsion and dipole-dipole attraction (QBECS) and with the local M-derivative of order α is introduced. Using similarity transformation, the generalized QBECS is transformed into the same system but with constant coefficients under certain conditions. Finally, the travelling wave transformation is used for getting rogue waves and soliton solutions for the original equation. The effect of the fractional order on the wave profile is discussed using some figures.

Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system

“…(1a) and (1b) is the ISM. It is successfully applied on partial differential equations and D Es [29][30][31][32] .…”

“…3 Basic Sciences Department, Mansoura Higher Institute for Engineering and Technology, Mansoura, Egypt. * email: abass_hassan@mans.edu.eg where is called the one-parameter Mitttag-Leffler function 18,19,32 . The M-fractional derivative has the same properties of classical derivatives in linearity, multiplication, and division of two functions but what distinguishes the M-fractional derivative are the following properties 18,19,32 :…”