title: Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.
abstract: We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
authors.forename: A
authors.initials: A
authors.lastname: Chowdury
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
authors.forename: D J
authors.initials: DJ
authors.lastname: Kedziora
authors.affiliation: Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia.
authors.forename: A
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: N
authors.initials: N
authors.lastname: Akhmediev
mesh_terms: D009038:Motion; D017711:Nonlinear Dynamics; D011789:Quantum Theory