1,721,007 research outputs found
Quasi-periodic solutions for completely resonant nonlinear wave equations in 1D and 2D
No full textWe provide quasi-periodic solutions with two frequencies for a class of completely resonant non-linear wave equations in one and two spatial dimensions and with periodic boundary conditions.
This is the first existence result for quasi-periodic solutions in
the completely resonant case. The main idea is to work in an appropriate invariant subspace, in order to simplify the bifurcation equation. The frequencies, close to that of the linear system, belong to an uncountable Cantor set of measure zero where no small divisor problem arises
Periodic solutions for nonlinear dispersive PDE's in d > 1 spatial dimensions
No full textwe describe a Lindestd series approach to the study of periodic solutions for classes of non linear PDE's in high spatial dimension. Our method covers allso various completely degenerate cases
Periodic solutions for the non linear wave equation on Lie Groups
No full textWe discuss periodic solutions of the non linear wave equation on compact manifolds. We prove the existence of families of periodic solutions on compact Lie groups
periodic solutions for NLS equations in high dimension
No full textWe discuss the construction of families of periodic solutions for the completely resonant NLS. In particular we analize the structure of the bifurcation equation
Periodic solutions for the non linear wave and Schrodinger equations on homogeneous manifolds
No full textWe prove the existence of families of periodic solutions on compact Lie groups and on homogeneous manifolds
ERC- Starting Grant
No full textprogetto di ricerca sulle applicazioni di metodi di piccoli divisori per le equazioni alle derviate parzial
periodic solutions for the regularizing NLS in d dimension
No full textwe show how the Lindstedt sereis approach can be generalized to construct periodic solutions for the NLS in d>1 dimansions
Exponentially small splitting and Arnold diffusion for multiple time scale system
No full textWe prove upper and lower bounds on the splitting for a class of a-priori stable Hamiltonian systems, in regions of the phase space characterized by one fast frequency. Finally using an appropriate Normal Form theorem we prove the existence of chains of heteroclinic intersections
A normal form for beam and non-local nonlinear Schrodinger equations
No full textWe discuss normal forms of the completely resonant nonlinear beam equation and nonlinear Schr?dinger equation. We work in n > 1 spatial dimensions and study both periodic and Dirichlet boundary conditions on cubes. We discuss the applications to the problem of finding quasi-periodic solutions. In the case of periodic boundary and the dimension n = 2, we apply KAM theory and prove the existence and stability of quasi-periodic solutions
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