313 citations · 906 across the 28 of their papers we have counts for
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Whitham modulation theory for (2+1)-dimensional equations of Kadomtsev-Petviashvili type
Mark J. Ablowitz, Gino Biondini, Igor Rumanov
Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev-Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP…
Whitham modulation theory for the two-dimensional Benjamin-Ono equation
Mark J. Ablowitz, Gino Biondini, Qiao Wang
Whitham modulation theory for the two dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasi-linear first-order partial differential equations is derived. Th…
Tight-binding methods for general longitudinally driven photonic lattices -- edge states and solitons
Mark J. Ablowitz, Justin T. Cole
A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are c…