Jaime Angulo Pava
This work presents new results about the instability of solitary-wave solutions to a generalized fifth-order Korteweg-deVries equation of the form
where for some which is homogeneous of degree for some . This model arises, for example, in the mathematical description of phenomena in water waves and magneto-sound propagation in plasma. The existence of a class of solitary-wave solutions is obtained by solving a constrained minimization problem in which is based in results obtained by Levandosky. The instability of this class of solitary-wave solutions is determined for , and it is obtained by making use of the variational characterization of the solitary waves and a modification of the theories of instability established by Shatah & Strauss, Bona & Souganidis & Strauss and Goncalves Ribeiro. Moreover, our approach shows that the trajectories used to exhibit instability will be uniformly bounded in .
Submitted August 13, 2002. Published January 10, 2003.
Math Subject Classifications: 35B35, 35B40, 35Q51, 76B15, 76B25, 76B55, 76E25.
Key Words: Water wave model, variational methods, solitary waves, instability.
Show me the PDF file (308K), TEX file, and other files for this article.
| Jaime Angulo Pava |
Department of Mathematics, IMECC-UNICAMP
C.P. 6065, CEP 13083-970-Campinas
Sao Paulo, Brazil
Return to the EJDE web page