Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

On three-dimensional generalizations of the Boussinesq and Korteweg-deVries equations


Author: E. Infeld
Journal: Quart. Appl. Math. 38 (1980), 277-287
MSC: Primary 35Q20; Secondary 76B25
DOI: https://doi.org/10.1090/qam/592196
MathSciNet review: 592196
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Three-dimensional generalizations of two different forms of the Boussinesq equation are derived. They are investigated for stability of slowly varying nonlinear wavetrains. The results obtained are then compared with the stability properties following from the full water wave equations. Agreement is found to be good for $ {h_0}{k_0}$ (depth times wavenumber) of order one. This is very satisfactory, as the Boussinesq equations are only supposed to be valid for small $ {h_0}{k_0}$. In particular, one version of the Boussinesq equation is found to yield instability with respect to one-dimensional perturbations for $ {h_0}{k_0} > 1.5$ (as against 1.36 for the full equations). Finally, a similar comparison is performed for the three-dimensional Korteweg--de Vries equation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35Q20, 76B25

Retrieve articles in all journals with MSC: 35Q20, 76B25


Additional Information

DOI: https://doi.org/10.1090/qam/592196
Article copyright: © Copyright 1980 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website