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A non-linear equation incorporating damping and dispersion

Published online by Cambridge University Press:  29 March 2006

R. S. Johnson
R. S. Johnson
Affiliation:
Department of Aeronautics, Imperial College Present address: School of Mathematics, University of Newcastle Upon Tyne.
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Abstract

The steady-state solution of the non-linear equation \[ h_t + hh_x + h_{xxx} = \delta h_{xx} \] with both damping and dispersion is examined in the phase plane. For small damping an averaging technique is used to obtain an oscillatory asymptotic solution. This solution becomes invalid as the period of the oscillation approaches infinity, and is matched to a straightforward expansion solution. The results obtained are compared with a numerical integration of the equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 1 , 4 June 1970 , pp. 49 - 60
Copyright
© 1970 Cambridge University Press

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References

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