The Christov-Galerkin spectral method in complex arithmetics

M. A. Christou; N. C. Papanicolaou; C. Sophocleous; C. I. Christov

doi:10.1063/1.5007420

The Christov-Galerkin spectral method in complex arithmetics

M. A. Christou, N. C. Papanicolaou, C. Sophocleous, C. I. Christov

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We apply the Christov-Galerkin spectral method for the numerical investigation of the interaction of solitons in the Cubic Nonlinear Schrödinger Equation. The issues of convergence are addressed and an algorithm is devised for the application of the method. Results are obtained for the interaction of solitons with different phase velocities and different carrier frequencies. The interactions are shown to be elastic, save for the phase shifts. The latter are extracted from the numerical solution and discussed.

Original language	English
Title of host publication	Application of Mathematics in Technical and Natural Sciences
Subtitle of host publication	9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017
Publisher	American Institute of Physics Inc.
Volume	1895
ISBN (Electronic)	9780735415799
DOIs	https://doi.org/10.1063/1.5007420
Publication status	Published - 12 Oct 2017
Event	9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017 - Albena, Varna, Bulgaria Duration: 21 Jun 2017 → 26 Jun 2017

Other

Other	9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017
Country/Territory	Bulgaria
City	Albena, Varna
Period	21/06/17 → 26/06/17

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10.1063/1.5007420

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Christou, M. A., Papanicolaou, N. C., Sophocleous, C., & Christov, C. I. (2017). The Christov-Galerkin spectral method in complex arithmetics. In Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017 (Vol. 1895). Article 120003 American Institute of Physics Inc.. https://doi.org/10.1063/1.5007420

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abstract = "We apply the Christov-Galerkin spectral method for the numerical investigation of the interaction of solitons in the Cubic Nonlinear Schr{\"o}dinger Equation. The issues of convergence are addressed and an algorithm is devised for the application of the method. Results are obtained for the interaction of solitons with different phase velocities and different carrier frequencies. The interactions are shown to be elastic, save for the phase shifts. The latter are extracted from the numerical solution and discussed.",

author = "Christou, {M. A.} and Papanicolaou, {N. C.} and C. Sophocleous and Christov, {C. I.}",

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Christou, MA , Papanicolaou, NC, Sophocleous, C & Christov, CI 2017, The Christov-Galerkin spectral method in complex arithmetics. in Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017. vol. 1895, 120003, American Institute of Physics Inc., 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017, Albena, Varna, Bulgaria, 21/06/17. https://doi.org/10.1063/1.5007420

The Christov-Galerkin spectral method in complex arithmetics. / Christou, M. A.; Papanicolaou, N. C.; Sophocleous, C. et al.
Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017. Vol. 1895 American Institute of Physics Inc., 2017. 120003.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We apply the Christov-Galerkin spectral method for the numerical investigation of the interaction of solitons in the Cubic Nonlinear Schrödinger Equation. The issues of convergence are addressed and an algorithm is devised for the application of the method. Results are obtained for the interaction of solitons with different phase velocities and different carrier frequencies. The interactions are shown to be elastic, save for the phase shifts. The latter are extracted from the numerical solution and discussed.

AB - We apply the Christov-Galerkin spectral method for the numerical investigation of the interaction of solitons in the Cubic Nonlinear Schrödinger Equation. The issues of convergence are addressed and an algorithm is devised for the application of the method. Results are obtained for the interaction of solitons with different phase velocities and different carrier frequencies. The interactions are shown to be elastic, save for the phase shifts. The latter are extracted from the numerical solution and discussed.

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BT - Application of Mathematics in Technical and Natural Sciences

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Christou MA , Papanicolaou NC, Sophocleous C, Christov CI. The Christov-Galerkin spectral method in complex arithmetics. In Application of Mathematics in Technical and Natural Sciences: 9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2017. Vol. 1895. American Institute of Physics Inc. 2017. 120003 doi: 10.1063/1.5007420

The Christov-Galerkin spectral method in complex arithmetics

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