2016 International Symposium on Nanofluid Heat and Mass Transfer in Textile Engineering and 5th International Symposium on Nonlinear Dynamics


Journal: Nonlinear Science Letters A
(ISSN 2519-9072(Online), ISSN 2076-2275 (Print))          Vol. 1 No. 1
An Exact, Periodic Solution of the Kaup-Newell Equation
K. W. Chow    
Department of Mechanical Engineering, University of Hong KongPokfulam, Hong Kong, China
Email: kwchow@hkusua.hku.hk
Abstract: An exact, periodic solution of a special derivative nonlinear Schrödinger model, the Kaup–Newell equation incorporating cubic nonlinearity, is derived. The polar, or Madelung, representation is employed. The amplitude and the phase are expressed in terms of elliptic function and elliptic integral of the third kind respectively. Insisting on strict periodicity for both the amplitude and phase yields a ‘quantized’, or ‘eigenvalue’, condition for the modulus of the elliptic functions. Plane wave and solitary pulses are recovered in the appropriate limiting regimes. For intermediate values of the modulus, numerical results are presented.

Keywords: Derivative nonlinear Schrödinger (Kaup-Newell) equation; Elliptic integrals of the third kind.

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