title: 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 Schrödinger 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.
authors.affiliation: Departamento de Física Fundamental, Universidad de Salamanca, E-37008 Salamanca, Spain.
authors.forename: P G
authors.initials: PG
authors.lastname: Estévez
authors.affiliation: GISC, Departamento de Física de Materiales, Universidad Complutense, E-28040 Madrid, Spain.
authors.forename: E
authors.initials: E
authors.lastname: Díaz
authors.affiliation: GISC, Departamento de Física de Materiales, Universidad Complutense, E-28040 Madrid, Spain.
authors.forename: F
authors.initials: F
authors.lastname: Domínguez-Adame
authors.affiliation: Departamento de Física Fundamental, Universidad de Salamanca, E-37008 Salamanca, Spain.
authors.forename: Jose M
authors.initials: JM
authors.lastname: Cerveró
authors.affiliation: Departamento de Física Fundamental, Universidad de Salamanca, E-37008 Salamanca, Spain.
authors.forename: E
authors.initials: E
authors.lastname: Diez