Lump solitons in a higher-order nonlinear equation in 2 + 1 dimensions

Abstract

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schr ̈ odinger
equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more
accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system
is derived after applying the singular manifold method. We also present an iterative procedure to construct the
solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.