Broken and unbroken solutions and dynamic behaviors for the mixed local–nonlocal Schrödinger equation. (July 2021)

• Record Type: Journal Article
• Authors: Yu, Fajun; Liu, Chunping; Li, Li
• Is Part Of: Applied mathematics letters. Volume 117(2021)
• Publication Date: 2021-07
• Subjects: Mixed-local–nonlocal nonlinear Schrödinger equation -- Soliton solutions -- Hirota's bilinearization transformation; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107075
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: Until now, the soliton solutions of nonlocal equations have also been put forward for the corresponding local equations. However, a natural motivation of our work is to find some soliton solutions to the mixed local–nonlocal equations that have not been reported for the associated nonlocal-type equations. A novel mixed local–nonlocal nonlinear Schrödinger (MLN-NLS) equation is presented, then we investigate the Hirota's bilinearization transformation and obtain the one- and two-soliton solutions of the MLN-NLS equation. Based on the obtained solutions, the propagation and interaction structures are shown, the broken and unbroken soliton solutions are derived with Hirota's transformation. We find that the MLN-NLS equation has some novel results, which is unlike the local or nonlocal cases. And these results seem to be the characteristic features of the mixed local–nonlocal nonlinear system in the present work.