Scientific Results

Periodic and solitary wave solutions of generalized nonlinear Schrodinger equation using a madelung fluid description

Year: 2010

Authors: Grecu D., Fedele R., De Nicola S., Grecu A.T., Visinescu A.

Autors Affiliation: Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering Horia Hulubei, Bucharest, RO-077125, Romania;
Dipartimento di Scienze Fisiche, Universita Federico II and INFN Sezione di Napoli, Napoli, Italy;
CNR – Istituto Nazionale di Ottica, Pozzuoli (NA), Italy

Abstract: The hydrodynamic fluid description, proposed many years ago by E. Madelung(1927) for quantum mechanics, is used to discuss the class of nonlinear Schrodinger equations. In the case of stationary profile solutions the equation satisfied by the fluid density ρ = j j2 is integrated and periodic solutions expressed through Jacobi elliptic functions are derived for cubic and cubic + quintic nonlinearities. In the limit case k2 = 1 the solitary wave solution found for the cubic + quintic nonlinearity proves tobe much steeper and narrower than the one-soliton solution of the cubic NLS equation.

Journal/Review: ROMANIAN JOURNAL OF PHYSICS

Volume: 55 (9-10)      Pages from: 980  to: 994

KeyWords: NONLINEAR EVOLUTION; PERIODIC SOLUTIONS; SOLITONS

Citations: 6
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English