title: Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.
abstract: We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
authors.forename: Adrian
authors.initials: A
authors.lastname: Ankiewicz
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
authors.forename: Yan
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Dipartimento di Ingegneria dell' Informazione, Università di Brescia, via Branze 38, 25123 Brescia, Italy.
authors.forename: Stefan
authors.initials: S
authors.lastname: Wabnitz
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
authors.forename: Nail
authors.initials: N
authors.lastname: Akhmediev