Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations

Abstract

Lump-type solutions, rationally localized in many directions in the space, are analyzed for nonlinear differential equations derived from generalized bilinear differential equations. By symbolic computations with Maple, positive quadratic and quartic polynomial solutions to two classes of generalized bilinear differential equations on [Formula: see text] are computed, and thus, lump-type solutions are presented to the corresponding nonlinear differential equations on [Formula: see text], generated from taking a transformation of dependent variables [Formula: see text].