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.

中文翻译：

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具有外部势的非自治部分非局部Gross-Pitaevskii方程的交叉Akhmediev和Ma呼吸器的激励管理

摘要

讨论了具有局部非局部非线性以及线性和抛物线电位的非自治Gross-Pitaevskii方程，并找到了非自治和自治方程之间的投影表达式。通过投影表达式并利用Darboux变换方法，得出了各种精确的解决方案，尤其是交叉的Akhmediev和Ma呼吸解。抛物线电位和线性电位分别影响相位线性调频和线性相位。通过选择衍射值，相位chi和波的初始宽度参数以改变累积时间的最大值，交叉的Akhmediev和Ma呼吸器的激励管理，包括不同部位的完整形状，高潮形状和早期形状的激励实现了交叉的Akhmediev和Ma呼吸器。