Volume 1, Issue 2
Solutions of the 1D Coupled Nonlinear Schrödinger Equations by the CIP-BS Method

Commun. Comput. Phys., 1 (2006), pp. 261-275.

Published online: 2006-01

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• Abstract

In this paper, we present solutions for the one-dimensional coupled nonlinear Schrödinger (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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@Article{CiCP-1-261, author = {}, title = {Solutions of the 1D Coupled Nonlinear Schrödinger Equations by the CIP-BS Method}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {2}, pages = {261--275}, abstract = {

In this paper, we present solutions for the one-dimensional coupled nonlinear Schrödinger (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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7957.html} }
TY - JOUR T1 - Solutions of the 1D Coupled Nonlinear Schrödinger Equations by the CIP-BS Method JO - Communications in Computational Physics VL - 2 SP - 261 EP - 275 PY - 2006 DA - 2006/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7957.html KW - AB -

In this paper, we present solutions for the one-dimensional coupled nonlinear Schrödinger (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.

T. Utsumi, T. Aoki, J. Koga & M. Yamagiwa . (2020). Solutions of the 1D Coupled Nonlinear Schrödinger Equations by the CIP-BS Method. Communications in Computational Physics. 1 (2). 261-275. doi:
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