New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential

Abstract

Solutions of the classical and nonlocal Gross-Pitaevskii (GP) equation with a parabolic potential and a gain term are derived by using a second order nonisospectral Ablowitz-Kaup-Newell-Segur system and reduction technique of double Wronskians. Solutions of the classical GP equation show typical space-time localized characteristics. An interesting dynamics, solitons carrying an oscillating wave, are found with mathematical analysis and illustrations. Solutions of some nonlocal cases are also illustrated.

21 pages, 7 figures

References in corpus (2)

• Integrable nonlocal asymptotic reductions of physically significant nonlinear equations
• Partially incoherent gap solitons in Bose-Einstein condensates

Cited by in corpus (4)

• The Fokas-Lenells equations: Bilinear approach
• Solutions to integrable space-time shifted nonlocal equations
• The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach
• Solutions to nonlocal nonisospectral (2+1)-dimensional breaking soliton equations