Soliton interactions on a boussinesq type equation with a linear restoring force

M. A. Christou

doi:10.1063/1.3659902

Soliton interactions on a boussinesq type equation with a linear restoring force

M. A. Christou

Department of Computer Science

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

Abstract

We study the propagation and interaction of solitons modeled by the equation governing the flexural deformation of an elastic rod on elastic foundation (EREFE). The model equation is only of fourth order, but because of the presence of the linear restoring force, it exhibits some of the phenomenology of the 6GBE, especially when the nonmonotonic shapes are concerned. To do that, we apply the Christov spectral method in L ²(-∞,∞). Initially, we solve the problem in the moving frame and consider the obtained solutions as initial condition for the time dependant problem and study the propagation and interaction of solitons.

Original language	English
Title of host publication	Application of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11
Pages	41-48
Number of pages	8
Volume	1404
DOIs	https://doi.org/10.1063/1.3659902
Publication status	Published - 2011
Event	3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11 - Albena, Bulgaria Duration: 20 Jun 2011 → 25 Jun 2011

Other

Other	3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11
Country/Territory	Bulgaria
City	Albena
Period	20/06/11 → 25/06/11

Keywords

Boussinesq
solitons
spectral method

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10.1063/1.3659902

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title = "Soliton interactions on a boussinesq type equation with a linear restoring force",

abstract = "We study the propagation and interaction of solitons modeled by the equation governing the flexural deformation of an elastic rod on elastic foundation (EREFE). The model equation is only of fourth order, but because of the presence of the linear restoring force, it exhibits some of the phenomenology of the 6GBE, especially when the nonmonotonic shapes are concerned. To do that, we apply the Christov spectral method in L 2(-∞,∞). Initially, we solve the problem in the moving frame and consider the obtained solutions as initial condition for the time dependant problem and study the propagation and interaction of solitons.",

keywords = "Boussinesq, solitons, spectral method",

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

year = "2011",

doi = "10.1063/1.3659902",

language = "English",

isbn = "9780735409767",

volume = "1404",

pages = "41--48",

booktitle = "Application of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11",

note = "3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11 ; Conference date: 20-06-2011 Through 25-06-2011",

}

Christou, MA 2011, Soliton interactions on a boussinesq type equation with a linear restoring force. in Application of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11. vol. 1404, pp. 41-48, 3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11, Albena, Bulgaria, 20/06/11. https://doi.org/10.1063/1.3659902

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T1 - Soliton interactions on a boussinesq type equation with a linear restoring force

AU - Christou, M. A.

PY - 2011

Y1 - 2011

N2 - We study the propagation and interaction of solitons modeled by the equation governing the flexural deformation of an elastic rod on elastic foundation (EREFE). The model equation is only of fourth order, but because of the presence of the linear restoring force, it exhibits some of the phenomenology of the 6GBE, especially when the nonmonotonic shapes are concerned. To do that, we apply the Christov spectral method in L 2(-∞,∞). Initially, we solve the problem in the moving frame and consider the obtained solutions as initial condition for the time dependant problem and study the propagation and interaction of solitons.

AB - We study the propagation and interaction of solitons modeled by the equation governing the flexural deformation of an elastic rod on elastic foundation (EREFE). The model equation is only of fourth order, but because of the presence of the linear restoring force, it exhibits some of the phenomenology of the 6GBE, especially when the nonmonotonic shapes are concerned. To do that, we apply the Christov spectral method in L 2(-∞,∞). Initially, we solve the problem in the moving frame and consider the obtained solutions as initial condition for the time dependant problem and study the propagation and interaction of solitons.

KW - Boussinesq

KW - solitons

KW - spectral method

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U2 - 10.1063/1.3659902

DO - 10.1063/1.3659902

M3 - Conference contribution

AN - SCOPUS:83655165330

SN - 9780735409767

VL - 1404

SP - 41

EP - 48

BT - Application of Mathematics in Technical and Natural Sciences - 3rd International Conference, AMiTaNS'11

T2 - 3rd International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS'11

Y2 - 20 June 2011 through 25 June 2011

ER -

Soliton interactions on a boussinesq type equation with a linear restoring force

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