6533b82dfe1ef96bd1291c79

RESEARCH PRODUCT

Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms

Philippe GreluFaiçal AzzouziHouria Triki

subject

PhysicsDirect numerical simulationAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsQuintic functionDipoleNonlinear systemsymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable SystemsClassical mechanicssymbolsUniquenessElectrical and Electronic EngineeringPhysical and Theoretical ChemistryMultipole expansionNonlinear Sciences::Pattern Formation and SolitonsNonlinear Schrödinger equationAnsatz

description

We consider a high-order nonlinear Schrodinger (HNLS) equation with third- and fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and dark solitary waves that allows us to obtain analytically different shapes of solitary wave solutions. Parametric conditions for the existence and uniqueness of such solitary waves are presented. The solutions comprise fundamental solitons, kink and anti-kink solitons, W-shaped, dipole, tripole, and fifth-order solitons. In addition, we found a new type of solitary wave solution that takes the shape of N, illustrating the potentially rich set of solitary wave solutions of the HNLS equation. Finally, the stability of the solutions is checked by direct numerical simulation.

yearjournalcountryeditionlanguage
2013-11-01Optics Communications
https://doi.org/10.1016/j.optcom.2013.06.039