Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics
Abstract
Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV6 equation are analysed. This allows for a formulation of conditions on the perturbation terms that preserve its integrability. The perturbation corrections to the scattering data and to the corresponding action-angle (canonical) variables are studied. The analysis shows that although many nontrivial solutions of KdV6 can be obtained by the Inverse Scattering Transform (IST), there are solutions that in principle can not be obtained via IST. Thus the equation in general is not completely integrable.
DOI
http://doi.org10.3934/cpaa.2012.11.1439
Recommended Citation
Gerdjikov, V., Grahovski, G., Ivanov, R.: On the integrability of KdV hierarchy with self-consistent sources, Commun. Pure Appl. Analysis, vol. 11 (2012), pp. 1439-1452. doi: 10.3934/cpaa.2012.11.1439
Funder
Science Foundation Ireland Grant 09/RFP/MTH2144
Included in
Dynamical Systems Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons
Publication Details
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
doi:10.3934/cpaa.2012.11.1439