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Chung-Hsien Tsai
Shy-Jen Guo



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Chung-Hsien Tsai
Shy-Jen Guo


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 17, 2018



The Bounded Solutions of a Fourth Order Model Equation

AUTHORS: Chung-Hsien Tsai, Shy-Jen Guo

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ABSTRACT: The objective of this paper is to construct bounded olutions of a model equation, which governs two dimensional steady capillary gravity waves of an ideal fluid flow with Bond number near 1/3 and Froude number close to one.

KEYWORDS: Lyapunov’s Center Theorem, Schauder fixed point theorem , Bounded Solution.

REFERENCES:

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[4] B. Buffoni, A.R. Champneys, A.R., Toland, J.F., ”Bifurcation and colescence of a plethora of homoclinic orbits for a Hamiltonian system,” Dyn. Differential Equations 8, 221 281 (1996)

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[8] Hunter J.K., and Vanden Broeck, J.M ., ”Solitary and periodic gravity capillary waves of finite amplitude,” . Fluid Mech. 134, 205 219 (1983)

[9] Iooss, G. & Kirchgässner, K. ”Water waves for small surface tension: an approach via norma form,” Proceedings of the Royal of Edinburgh 122A, 267 299 (1992)

[10] Korteweg, P.J. and de Vries, G. ”On the change of the form of long waves advancing in a rectangular canal, and on a new type of long stationary waves,” Phil. Mag. 39, 422 443 (1895)

[11] Markeev, A.P. ”Stability of a canonical system with two degrees of freedom in the presence of resonance,” Journals of Applied Mathematics and Mechanics 32, 766 722 (1968)

[12] Merkin, D.R. ”Intrduction to the Theory of Stability,” Springer Verlag, TAM 24, (1997)

[13] Meyer, K.R. & Hall, G.R. ”Intrduction to Hami ltonian Dynamical Systems and the N Body Problem,” Springer Verlag, 90, (1990)

[14] Peters, A.D.; Stoker, J.J. ”Solitary waves in liquids having non constant density.,” Comm. Pure Appl. Math. 13, 115 164 (1960)

[15] Sokol’skii, A.G. ”On the stability of an autono mous Hamiltonian system with two degrees of freedom in the case of equal frequencies,” J. Appl. Math.Mech., 38, 741 749 (1975)

[16] Tsai, Chung Hsien & Guo, Shy Jen ” The stability of zero solution of a model equation for steady capillary gravity waves with the bond number close to 1/3.,” Proceedings of the th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09), pp.90 93, Ningbo, China anuary 10 12 2009

[17] Tsai, Chung Hsien & Guo, Shy Jen ” Unsymmetric Solitary Wave Solutions of a Fifth Order Model Equation for Steady Capillary Gravity Waves over a Bump with the Bond Number Near 1/3 ” Proceedings of the th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09 pp.94 99, Ningbo, China anuary 10 12 2009

[18] Tsai, Chung Hsien & Guo, Shy Jen ”Stability of Fixed Points of a Fifth Order Equation,” 18th International Conference on APPLIED MATHEMATICS (AMATH '13), pp.94 99, Budapest, Hungary December 89 93 (2013).

[19] Zufiria, J.A. ”Weakly nonlinear non symmetric gravity waves on water of finite depth,” J. fluid Mech. 180, 371 385 (1987)

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #14, pp. 93-100


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