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International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 599-604
http://dx.doi.org/10.1155/S0161171297000811

Wave growth patterns in a non-linear dispersive system with instability and dissipation

1Department of Mechanical & Aerospace Engineering, West Virginia University, Morgantown 26506, WV, USA
2CFC, Department of Civil Engineering, West Virginia University, Morgantown 26506, WV, USA

Received 30 November 1995

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A simple one-dimensional non linear equation including effects of instability, dissipation, and dispersion is examined numerically. Periodic solution of a non linear dispersive equation is presented for different values of α, β, and γ characterizing the constants for instability, dissipation, and dispersion respectively. In this paper, the growth pattern for the wave at different time intervals is discussed. Various equilibrium states with different initial configuration have been observed depending on initial conditions.