Paper title: From the Boussinesq-type Equation to the Static Beam Equation
DOI: https://doi.org/10.4316/JACSM.201902008
Published in: Issue 2, (Vol. 13) / 2019Download
Publishing date: 2019-12-16
Pages: 50-52
Author(s): BOKOLO R. Gilles
Abstract. In this paper we investigate the Hopf-Cole transformation to solve the Boussinesq-type equation. As a by-product, a linearization of the later will generate the static beam equation. Hence, we prove that soliton-type solutions profiles are preserved.
Keywords: Boussinesq-type Equation, Static Beam Equation, Hopf-Cole Transformation, Solitons
References:

1. An Lianjun and A. Piere, “A weakly nonlinear analysis of elasto-plastic-microstructure models”, SIAM J.Appl.Math.55, pp.136-155,1995

2. E.A.Witmer, “Elementary Bernoulli-Euler Beam theory”, MIT Unified Engineering Course Notes, pp.5-114

3. Guowang CHEN and Zhijian YANG, “On the initial boundary value problems of the fourth order nonlinear wave equation and the Boussinesq type equation”, proceeding of the conference on Nonlinear Partial Equations and Applications, pp. 20-26, 2002

4. J.Boussinesq, “Essaie sur la théorie des eaux courantes”, Comptes rendus de l’academie des sciences, vol.23, p.1-680,1877

5. J.Boussinesq, “Théorie des ondes et des remous qui se propagent le long d’un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond”, Journal de mathematiques pures et appliquées, vol.17, p.55-108,1872

6. J.L.Bona; W.G.Pritchard;L.R.Scott, “Solitary-wave interaction”, Physics of Fluids, 23(3), pp.438-441, 1980

7. M.Remoissenet, “waves called solitons: Concepts and experiements”, Springer, pp.11, 1999

8. Muthukrishnan Sathyamoorthy, “Nonlinear Analysis Structures”, CRC Press, 1998, pp. 1–73.

9. R.Gilles Bokolo, “Hopf-Cole transformation with effect of the dissipation coefficient on nonlinearity in the Benjamin-Bona-Mahony (BBM) generalized pseudo-parabolic equation”, International journal of Science and research (IJSR), volume 8 issue 6, pp.1707-1710, 2019

Back to the journal content
Creative Commons License
This article is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
Home | Editorial Board | Author info | Archive | Contact
Copyright JACSM 2007-2020