Diverse partially nonlocal bright–dark Peregrine “three sisters” excitations in a (3+1)-dimensional vector nonlinear Schrödinger equation

Abstract

This paper aims to analyze diverse excitations of partially nonlocal bright–dark Peregrine “three sisters” based on a nonautonomous (3+1)-dimensional vector partially nonlocal nonlinear Schrödinger equation with different diffractions in two horizontal directions by simplifying into an autonomous vector nonlinear Schrödinger equation, whose solutions are exploited to produce analytical solutions of the nonautonomous vector equation via the nonrecursive Darboux method. Diverse excitations of partially nonlocal bright–dark Peregrine “three sisters” are discussed in an exponential diffraction system by comparing two values of maximum accumulated time with the excited time for Peregrine “three sisters”. When the value of the x or y-directional diffraction is fixed, with the increase of the magnitude of the initial y or x-directional diffraction, the amplitude of fully or nascently excited bright–dark Peregrine structures increases and their widths both decrease in the exponential system. This investigation gives a deeper knowledge for partially nonlocal solitons in the versatile fields of optical engineering, ocean engineering and other engineering disciplines.

Keywords

• (3+1)-dimensional vector nonlinear Schrödinger equation
• Partially nonlocal bright–dark peregrine “three sisters”
• Different diffractions in two horizontal directions