Excitation management of crossed Akhmediev and Ma breather for a nonautonomous partially nonlocal Gross–Pitaevskii equation with an external potential

Abstract

A nonautonomous Gross–Pitaevskii equation with a partially nonlocal nonlinearity and a linear and parabolic potential is discussed, and a projecting expression between nonautonomous and autonomous equations is found. Via the projecting expression and utilizing the Darboux transformation method, diversified exact solutions, especially including a crossed Akhmediev and Ma breather solution, are engendered. The parabolic and linear potentials influence the phase chirp and linear phase, respectively. By selecting values of diffraction, phase chirp and initial width parameters of wave to vary the maximum value of the accumulated time, the excitation management of the crossed Akhmediev and Ma breather, including the excitations of full shape, climax shape and early shape for different parts of the crossed Akhmediev and Ma breather, is achieved.