Approximate solution of the Kuramoto-Shivashinsky equation on an unbounded domain

Wael W. Mohammed1,2
1Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
2Department of Mathematics, Faculty of Science, Hail University, Hail, Saudi Arabia

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Tài liệu tham khảo

Adams, R. A., Sobolev spaces, Academic Press, New York, 1975.

Adams, D. R. and Hedberg, L. I., Function Spaces and Potential Theory, Springer-Verlag, 1996.

Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston and London, 1994.

Alizadeh-Pahlavan, A., Aliakbar, V., Vakili-Farahani, F. and Sadeghy, K., MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method, Commun. Nonlinear Sci. Numer. Simul., 14, 2009, 47388.

Awrejcewicz, J., Andrianov, I. V. and Manevitch, L. I., Asymptotic Approaches in Nonlinear Dynamics, Springer-Verlag, Berlin, 1998.

Baldwin, D., Goktas, O., Hereman, W., et al., Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs, J. Symbolic Comput., 37, 2004, 669–705.

Benney, D. J., Long waves on liquid films, J. Math. Phys., 45, 1966, 150–155.

Collet, P. and Eckmann, J. P., The time dependent amplitude equation for the Swift-Hohenberg problem, Comm. Math. Physics., 132, 1990, 139–153.

He, J. H., Homotopy perturbation technique, Comput. Meth. Appl. Mech. Eng., 178, 1999, 25762.

Hooper, A. P. and Grimshaw, R., Nonlinear instability at the interface between two fluids, Phys. Fluids, 28, 1985, 37–45.

Kuramoto, Y., Diffusion-induced chaos in reaction systems, Suppl. Prog. Theor. Phys, 64, 1978, 346–367.

Kuramoto, Y. and Tsuzuki, T., On the formation of dissipative structures in reaction diffusion systems, Prog. Theor. Phys., 54, 1975, 687–699.

Kuramoto, Y. and Tsuzuki, T., Persistent propogation of concentration waves in dissipative media far from thermal equilibrium, Prog. Theor. Phys., 55, 1976, 356–369.

Liao, S. J., A kind of approximate solution technique which does not depend upon small parameters (II): An application in fluid mechanics, Int. J. Nonlinear Mech., 32(8), 1997, 1522.

Ma, W. X. and Fuchssteiner, B., Integrable theory of the perturbation equations, Chaos, Solitons & Fractals, 7(8), 1996, 1227–1250.

Mielke, A. and Schneider, G., Attractors for modulation equations on unbounded domains-existence and comparison, Nonlinearity, 8, 1995, 743–768.

Mielke, A., Schneider, G. and Ziegra, A., Comparison of inertial manifolds and application to modulated systems, Math. Nachr., 214, 2000, 53–69.

Runst, T. and Sickel, W., Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, Walter de Gruyter, Berlin, New York, 1996.

Sajid, M., Hayat, T., Comparison of HAM and HPM methods for nonlinear heat conduction and convection equations, Nonlinear Anal: Real World Appl., 9, 2008, 2296301.

Schneider, G., A new estamite for the Ginzburg-Landau approximation on the real axis, J. Nonlinear Science, 4, 1994, 23–34.

Schneider, G., The validity of generalized Ginzburg-Landau equations, Math. Methods Appl. Sci., 19(9), 1996, 717–736.

Sivashinsky, G. I., Nonlinear analysis of hydrodynamic instability in laminar flames I: Derivation of basic equations, Acta Astronau, 4, 1977, 1177–1206.

Sivashinsky, G. I., Instabilities, pattern formation, and turbulence in flames, Annu. Rev. Fluid Mech., 15, 1983, 179–199.

Shlang, T. and Sivashinsky, G. I., Irregular flow of a liquid film down a vertical column, J. Phys., 43, 1982, 459–466.

Van Gorder, R. A. and Vajravelu, R. A., Analytic and numerical solutions to the Lane-Emden equation, Phys. Lett. A, 372, 2008, 60605.

Von Dyke, M., Perturbation Methods in Fluid Mechanics, The Parabolic Press, Stanford, California, 1975.

Yabushita, K., Yamashita, M. and Tsuboi, K., An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method, J. Phys. A, 40, 2007, 840316.

Zhu, S. P., A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield, ANZIAM J., 47, 2006, 47794.