Christov-galerkin expansion for localized solutions in model equations with higher order dispersion

M. A. Christou

doi:10.1063/1.2806043

Christov-galerkin expansion for localized solutions in model equations with higher order dispersion

M. A. Christou

Department of Computer Science

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

Abstract

We develop a Galerkin spectral technique for computing localized solutions of equations with higher order dispersion. To this end, the complete orthonormal system of functions in L²(-∞,∞) proposed by Christov [1] is used. As a featuring example, the Sixth-Order Generalized Boussinesq Equation (6GBE) is investigated whose solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). Localized solutions are obtained here numerically for the case of the moving frame which are used as initial conditions for the time dependent problem.

Original language	English
Title of host publication	APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS'33
Subtitle of host publication	33rd International Conference
Pages	91-98
Number of pages	8
Volume	946
DOIs	https://doi.org/10.1063/1.2806043
Publication status	Published - 2007
Event	33rd International Conference on Applications of Mathematics in Engineering and Economics - Sozopol, Bulgaria Duration: 8 Jun 2007 → 14 Jun 2007

Other

Other	33rd International Conference on Applications of Mathematics in Engineering and Economics
Country/Territory	Bulgaria
City	Sozopol
Period	8/06/07 → 14/06/07

Keywords

Boussinesq equation
CCON system
Christov-Galerkin
Spectral methods

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10.1063/1.2806043

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title = "Christov-galerkin expansion for localized solutions in model equations with higher order dispersion",

abstract = "We develop a Galerkin spectral technique for computing localized solutions of equations with higher order dispersion. To this end, the complete orthonormal system of functions in L2(-∞,∞) proposed by Christov [1] is used. As a featuring example, the Sixth-Order Generalized Boussinesq Equation (6GBE) is investigated whose solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). Localized solutions are obtained here numerically for the case of the moving frame which are used as initial conditions for the time dependent problem.",

keywords = "Boussinesq equation, CCON system, Christov-Galerkin, Spectral methods",

author = "Christou, \{M. A.\}",

year = "2007",

doi = "10.1063/1.2806043",

language = "English",

isbn = "0735404607",

volume = "946",

pages = "91--98",

booktitle = "APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS'33",

note = "33rd International Conference on Applications of Mathematics in Engineering and Economics ; Conference date: 08-06-2007 Through 14-06-2007",

}

Christou, MA 2007, Christov-galerkin expansion for localized solutions in model equations with higher order dispersion. in APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS'33: 33rd International Conference. vol. 946, pp. 91-98, 33rd International Conference on Applications of Mathematics in Engineering and Economics, Sozopol, Bulgaria, 8/06/07. https://doi.org/10.1063/1.2806043

TY - GEN

T1 - Christov-galerkin expansion for localized solutions in model equations with higher order dispersion

AU - Christou, M. A.

PY - 2007

Y1 - 2007

N2 - We develop a Galerkin spectral technique for computing localized solutions of equations with higher order dispersion. To this end, the complete orthonormal system of functions in L2(-∞,∞) proposed by Christov [1] is used. As a featuring example, the Sixth-Order Generalized Boussinesq Equation (6GBE) is investigated whose solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). Localized solutions are obtained here numerically for the case of the moving frame which are used as initial conditions for the time dependent problem.

AB - We develop a Galerkin spectral technique for computing localized solutions of equations with higher order dispersion. To this end, the complete orthonormal system of functions in L2(-∞,∞) proposed by Christov [1] is used. As a featuring example, the Sixth-Order Generalized Boussinesq Equation (6GBE) is investigated whose solutions comprise monotone shapes (sech-es) and damped oscillatory shapes (Kawahara solitons). Localized solutions are obtained here numerically for the case of the moving frame which are used as initial conditions for the time dependent problem.

KW - Boussinesq equation

KW - CCON system

KW - Christov-Galerkin

KW - Spectral methods

UR - https://www.scopus.com/pages/publications/36849095416

U2 - 10.1063/1.2806043

DO - 10.1063/1.2806043

M3 - Conference contribution

AN - SCOPUS:36849095416

SN - 0735404607

SN - 9780735404601

VL - 946

SP - 91

EP - 98

BT - APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS'33

T2 - 33rd International Conference on Applications of Mathematics in Engineering and Economics

Y2 - 8 June 2007 through 14 June 2007

ER -

Christov-galerkin expansion for localized solutions in model equations with higher order dispersion

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