Partially Integrable Evolution Equations in Physics

Partially Integrable Evolution Equations in Physics

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In the many physical phenomena ruled by partial differential equations, two extreme fields are currently overcrowded due to recent considerable developments: 1) the field of completely integrable equations, whose recent advances are the inverse spectral transform, the recursion operator, underlying Hamiltonian structures, Lax pairs, etc 2) the field of dynamical systems, often built as models of observed physical phenomena: turbulence, intermittency, Poincare sections, transition to chaos, etc. In between there is a very large region where systems are neither integrable nor nonintegrable, but partially integrable, and people working in the latter domain often know methods from either 1) or 2). Due to the growing interest in partially integrable systems, we decided to organize a meeting for physicists active or about to undertake research in this field, and we thought that an appropriate form would be a school. Indeed, some of the above mentioned methods are often adaptable outside their original domain and therefore worth to be taught in an interdisciplinary school. One of the main concerns was to keep a correct balance between physics and mathematics, and this is reflected in the list of courses.In the low amplitude limit the spin dynamics can be modeled by NLS-like equations, this point will be also shortly examined. 4.1. SPIN CHAINS ... The quantities g and uB are respectively the LandAc factor and the Bohr magneton. The dynamicsanbsp;...

Title:Partially Integrable Evolution Equations in Physics
Author:R. Conte, N. Boccara
Publisher:Springer Science & Business Media - 2012-12-06


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