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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov
Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov
Conference papers
The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of different G-strand …
Integrability, Recursion Operators And Soliton Interactions, Boyka Aneva, Georgi Grahovski, Rossen Ivanov, Dimitar Mladenov
Integrability, Recursion Operators And Soliton Interactions, Boyka Aneva, Georgi Grahovski, Rossen Ivanov, Dimitar Mladenov
Book chapter/book
This volume contains selected papers based on the talks,presentedat the Conference Integrability, Recursion Operators and Soliton Interactions, held in Sofia, Bulgaria (29-31 August 2012) at the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences. Included are also invited papers presenting new research developments in the thematic area. The Conference was dedicated to the 65-th birthday of our esteemed colleague and friend Vladimir Gerdjikov. The event brought together more than 30 scientists, from 6 European countries to celebrate Vladimir's scientific achievements. All participants enjoyed a variety of excellent talks in a friendly and stimulating atmosphere. …
Examples Of G-Strand Equations, Darryl Holm, Rossen Ivanov
Examples Of G-Strand Equations, Darryl Holm, Rossen Ivanov
Conference papers
The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincare´ reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of G-strand constructions, including …
Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems, Vladimir Gerdjikov, Rossen Ivanov, Gaetano Vilasi
Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems, Vladimir Gerdjikov, Rossen Ivanov, Gaetano Vilasi
Articles
We are analyzing several types of dynamical systems which are both integrable and important for physical applications. The first type are the so-called peakon systems that appear in the singular solutions of the Camassa-Holm equation describing special types of water waves. The second type are Toda chain systems, that describe molecule interactions. Their complexifications model soliton interactions in the adiabatic approximation. We analyze the algebraic aspects of the Toda chains and describe their real Hamiltonian forms.