Abstract
We study a nonautonomous (2+1)-dimensional coupled partially nonlocal nonlinear Schrödinger equation under a linear and parabolic potential, and find a mapping expression between nonautonomous and autonomous equations. Via this mapping equation with the Darboux method, we find diversified exact solutions, such as scalar and vector crossed breather-pair. By changing values of phase chirp and diffraction parameters to alter value of maximal cumulative time and compare with values of top position, we investigate the controlling excitation of scalar and vector crossed breathers including the early shape, top shape, entire shape and periodical reproduction excitations in different external potentials.
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