We exhibit the bi-Hamiltonian structure of the equations of associativity (Witten-Dijkgraaf-Verlinde-Verlinde-Dubrovin equations) in 2-d topological field theory, which reduce to a single equation of Monge-Ampegravere type f ttt=f xxt2-f xxxf xtt, in the case of three primary fields. The ...
释义: 全部 更多例句筛选 1. New Lax Integrable Hierarchy of Evolution Equations and Its Infinite-Dimensional Bi-Hamiltonian Structure 新的Lax可积发展方程族及其无限维双-哈密顿结构 www.ilib.cn 2. A New Integrable System and Its Bi-Hamiltonian Structure 一族新的可积系及其双哈密顿结构 www.ilib.cn...
3 The bi-hamiltonian structure In order to get variables of separation according to general usage of bi-hamiltonian geometry firstly we have to calculate the bi-hamiltonian structure for the given integrable system with integrals of motion H1,2 (2.5) on the Poisson manifold so(4) with the ...
These carry the structure of a Frobenius algebra on each tangent space, but will, in general, be curved. The induced curvature is studied, a main result being that these natural submanifolds carry a induced pencil of compatible metrics. It is then shown how one may constrain the bi-...
Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux trans... A spectral problem and the associated Gerdjikov鈥揑vanov (GI) hierarchy of nonlinear evolution equations is presented. As a reduction, the well...
A second Poisson bracket structure can be obtained from the recursion operator R = P 2 P −1 1 (1.8) leading to P 2 (x, y) = 0δ im δ lj 0 ∂ x δ(x −y) + (1.9) r i (x)r j (y) +r j (x)r i (y) −δ im k r k (x)q k (y) −r i (x)q m...
has the bihamiltonian structure {w(x), w(y)} 1 =δ ′ (x −y), {w(x), w(y)} 2 = w(x)∂ x + 1 2 w x + ǫ 2 8 ∂ 3 x δ(x −y). (1.9) The first nontrivial equation of the hierarchy is the KdV equation w t = ww x + ǫ 2 12 w xxx . (1.10...
摘要: A method of generating a MMGD (Magri–Morosi-Gel'fand–Dorfman) bi-Hamiltonian structure leading to complete integrability of the associated Hamiltonian system is presented. The Hamiltonian formalism is defined in terms of the fundamental notions of the Poisson calculus. 关键词: Poisson calcul...
Lerman L.M., Umanskij Ya.L.: The structure of the Poisson action of \({{\mathbb{R}}^2}\) on a four-dimensional symplectic manifold. II. Sel. Math. Sov. 7(1), 39–48 (1988) MATH Google Scholar Miranda E., Zung Nguyen Tien.: Equivariant normal form for nondegenerate singular ...
We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure whic... I Zakharevich - arXiv Mathematics e-prints 被引量: 0发表: 1999年 Veronese webs for bihamiltonian structures of higher corank It is shown ...