Exact solitary waves in a convecting fluid
- 7 June 1991
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 24 (11) , L587-L590
- https://doi.org/10.1088/0305-4470/24/11/003
Abstract
The perturbed Korteweg-de Vries equation ut+ lambda 1uux+ lambda 2uxxx+ lambda 3uxxxx+ lambda 4 (uux)x+ lambda 5uxx=0, which describes the evolution of long shallow waves in a convecting fluid when the critical Rayleigh number slightly exceeds its critical value, admits two types of exact solitary wave solution.Keywords
This publication has 7 references indexed in Scilit:
- Exact solutions of the generalized Kuramoto-Sivashinsky equationPhysics Letters A, 1990
- Evolution equation of surface waves in a convecting fluidPhysical Review A, 1990
- Painleve analysis and Backlund transformation in the Kuramoto-Sivashinsky equationJournal of Physics A: General Physics, 1989
- On the weakly nonlinear evolution of a perturbed planar solid-liquid interfacePhysica D: Nonlinear Phenomena, 1987
- Formation of Saturated Solitons in a Nonlinear Dispersive System with Instability and DissipationPhysical Review Letters, 1983
- The Painlevé property for partial differential equationsJournal of Mathematical Physics, 1983
- Instabilities, Pattern Formation, and Turbulence in FlamesAnnual Review of Fluid Mechanics, 1983