Abstract
Hierarchies of Peregrine solution and breather solution are derived in a (2+1)-dimensional variable-coefficient nonlinear Schrodinger equation with partial nonlocality. Based on these solutions, we study the control of the excitation of Peregrine solution and breather solution in different planes. In particular, the localized Peregrine solution and breather solution are firstly reported in two-dimensional space. It is expected that our analysis and results may give new insight into higher-dimensional localized rogue waves in nonlocal media.
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