Using the Continuous Spectrum to "Feel" Integrability: the Effect of Boundary Conditions

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The scope of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE). For monoparametric families of PDE/DDE's, that are known to possess isolated integrable points, we find that very special features occur in the continuous (``phonon'') spectrum at these ``singular'' points. We identify these features in the case example of a PDE and a DDE (that sustain front and pulse-like solutions respectively) for different types of boundary conditions. The key finding of the work is that such spectral features are generic near the singular, integrable points and hence we propose to explore a given PDE/DDE for such traits, as a means of assessing its potential integrability.
5 pages, 5 figures, submitted to PRE

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Exactly Solvable and Integrable Systems, Pattern Formation and Solitons

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http://salesiana.dossiersoluciones.com/handle/123456789/80379

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0212035
 http://arxiv.org/abs/nlin/0212035

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arXiv