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A generalized nonlocal nonlinear Hirota (GNNH) equation with variable coefficients is presented, which can be reduced into the nonlocal Hirota equation with the self-induced PT-symmetric potential. Especially, the nonlocal Gross–Pitaevskii (NGP) equation with the self-induced PT-symmetric potential is derived from the GNNH equation. Then, we obtain some novel non-autonomous breather solutions and...
A binary Darboux transformation for the nonlocal Davey–Stewartson II equation is constructed by the Darboux matrix method. As applications, N-soliton, breather and lump solutions of the considered equation have been obtained. In particular, the dynamics of the single soliton, two-soliton, breather and lump solutions are discussed and illustrated through some figures.
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