Solutions of the 1D Coupled Nonlinear Schrödinger Equations by the CIP-BS Method
Takayuki Utsumi 1*, Takayuki Aoki 2, James Koga 3, Mitsuru Yamagiwa 31 Department of Electronics and Computer Science, Tokyo University of Science, Yamaguchi, 1-1 Daigaku-dori, Sanyou-Onoda, Yamaguchi 756-0884, Japan.
2 Global Scientific Information and Computing Center, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan.
3 Japan Atomic Energy Agency, 8-1 Umemidai Kizu-cho, Souraku-gun, Kyoto 619-0215, Japan.
Received 30 August 2005; Accepted (in revised version) 25 November 2005
Communicated by Takashi Yabe
In this paper, we present solutions for the one-dimensional coupled nonlinear Schrodinger (CNLS) equations by the Constrained Interpolation Profile - Basis Set (CIP-BS) method. This method uses a simple polynomial basis set, by which physical quantities are approximated with their values and derivatives associated with grid points. Nonlinear operations on functions are carried out in the framework of differential algebra. Then, by introducing scalar products and requiring the residue to be orthogonal to the basis, the linear and nonlinear partial differential equations are reduced to ordinary differential equations for values and spatial derivatives. The method gives stable, less diffusive, and accurate results for the CNLS equations.
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Key words: The CIP-BS method; basis set; differential algebra; the Galerkin method; the coupled nonlinear Schrodinger equation.
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Correspondence to: Takayuki Utsumi , Electronics and Computer Science, Tokyo University of Science, Yamaguchi, 1-1 Daigaku-dori, Sanyou-Onoda, Yamaguchi, 756-0884, Japan. Email: firstname.lastname@example.org