Variational Principle for Traveling Waves in a Modified Kuramoto-Sivashinsky Equation

Erni Laswinda, Mahdhivan Syafwan, Arrival Rince Putri

Abstract


In this paper, variational principle for traveling waves in a modified Kuramoto-Sivashinsky equation is constructed by the semi-inverse method. We confirm that the method is very effective and gives the results in the concise form of variational functionals.


Keywords


Kuramoto-Sivashinsky equation, variational principle, semi-inverse method

Full Text:

PDF

References


Khater, A. H., Moussa, M. H. M and Abdul-Aziz, S. F. 2003. Invariant Variational Principles and Conservation Laws for Some Nonlinear Partial Differential Equations with Constant Coefficients–II. Chaos, Solitons & Fractals. 15, 1–13.

He, Ji-Huan. 1997. Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics. Int. J. Turbo Jet-Engines 14(1), 23–8.

Xu, L. 2006. Variational Principles for Coupled Nonlinear Schrodinger Equations. Physics Letters A. 359, 627-629.

Yao, L., Yang, Yun-Jie and Zhou, Xing-Wei. 2013. A Note on the Semi-Inverse Method and a Variational Principle for the Generalized KdV-mKdV Equation. Abstract and Applied Analysis, Vol. 2013 Article ID 931643.

He, Ji-Huan. 2004. Variational Princple for Some Nonlinear Partial Differential Equations with Variable Coefficients. Chaos, Solitons dan Fractals. 19, 847-851.

Hazewinkel, M. 2001. Encyclopaedia of Mathematics: Supplement III. Kluwer Academic Publishers: Dordrecht.

Kuramoto, Y. 1978. Diffusion-Induced Chaos in Reaction System. Progr. Theor. Phys. Suppl. 64. 346-367.

Sivashinsky, G. I. 1977. Nonlinear Analysis of Hydrodynamic Instability in Laminar Flames-I. Derivation of Basic Equations. Acta Astronautica 4. 4, 1177-1206.




DOI: http://dx.doi.org/10.52155/ijpsat.v17.1.1352

Refbacks

  • There are currently no refbacks.


Copyright (c) 2019 Erni Laswinda, Mahdhivan Syafwan, Arrival Rince Putri

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.