| Full text | |
| Author(s): |
Pava, Jaime Angulo
Total Authors: 1
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| Document type: | Journal article |
| Source: | Electronic Journal of Differential Equations; v. N/A, p. 18-pg., 2003-01-01. |
| Abstract | |
This work presents new results about the instability of solitary-wave solutions to a generalized fifth-order Korteweg-deVries equation of the form [GRAPHICS] where G(q, r, s) = F-q(q, r) - rF(qr)(q, r) - sF(rr)(q, r) for some F(q, r) which is homogeneous of degree p + 1 for some p > 1. 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 H-2(R) which is based in results obtained by Levandosky. The instability of this class of solitary-wave solutions is determined for b not equal 0, 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 H-2(R). (AU) | |