WebDec 1, 2006 · We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations (PDEs). The theorem applies to semilinear equations with nonlinearity satisfying a property that we call tame modulus. Such a property is related to the classical tame inequality by Moser. In the nonresonant case we deduce that any small amplitude … WebMay 1, 2024 · Request PDF An Abstract Birkhoff Normal Form Theorem and Exponential Type Stability of the 1d NLS We study stability times for a family of parameter dependent nonlinear Schrödinger equations ...
Convergence or generic divergence of the Birkhoff normal form
WebFeb 12, 2024 · More precisely, we prove a rigorous reduction of the water waves equations to its integrable Birkhoff normal form up to order 4. As a consequence, we also obtain … WebAn abstract Birkhoff normal form theorem is constructed for infinite dimensional Hamiltonian systems with unbounded perturbations. It is shown, for a class of derivative nonlinear Schrödinger equations, that any solution with small initial value remains small in high index Sobolev norm over a long time. smart cabs
Convergence or Generic Divergence of the Birkhoff Normal …
WebJun 1, 2011 · The concept of Birkhoff–Gustavson normal forms led to several applications [2,9,17]. We mention the article [8] as refer- ce to an algorithm of reduction to the Birkhoff normal form. M. Gutzwiller [12] in his book emphasized the importance the method of normal forms in different semiclassical constructions. For other applications of the ... WebDec 1, 2006 · We prove an abstract Birkhoff normal form theorem for Hamiltonian Partial Differential Equations. The theorem applies to semilinear equations with nonlinearity satisfying a property that we call of Tame Modulus. Such a property is related to the classical tame inequality by Moser. In the nonresonant case we deduce that any small … WebThe framework of symmetry provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. smart cabs reading