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pro vyhledávání: '"Kuksin, Sergei B"'
In this paper we prove a KAM theorem for small-amplitude solutions of the non linear beam equation on the d-dimensional torus $$u_{tt}+\Delta^2 u+m u + \partial_u G(x,u)=0\ ,\quad t\in { \mathbb{R}} , \; x\in \ { \mathbb{T}}^d, \qquad \qquad (*) $$ w
Externí odkaz:
http://arxiv.org/abs/1604.01657
We prove an abstract KAM theorem adapted to space-multidimensional hamiltonian PDEs with regularizing nonlinearities. It applies in particular to the singular perturbation problem studied in the first part of this work.
Externí odkaz:
http://arxiv.org/abs/1502.02262
In this paper we prove a KAM result for the non linear beam equation on the d-dimensional torus $$u_{tt}+\Delta^2 u+m u + g(x,u)=0\ ,\quad t\in { \mathbb{R}} , \; x\in {\mathbb T}^d, \qquad \qquad (*) $$ where $g(x,u)=4u^3+ O(u^4)$. Namely, we show t
Externí odkaz:
http://arxiv.org/abs/1412.2803
Autor:
Kuksin, Sergei B.
We consider the linear Schr\"odinger equation under periodic boundary condition, driven by a random force and damped by a quasilinear damping: $$ \frac{d}{dt}u+i\big(-\Delta+V(x)\big) u=\nu \Big(\Delta u-\gr |u|^{2p}u-i\gi |u|^{2q}u \Big) +\sqrt\nu\,
Externí odkaz:
http://arxiv.org/abs/1106.1158
Autor:
Kuksin, Sergei B.
For the damped-driven KdV equation $$ \dot u-\nu{u_{xx}}+u_{xxx}-6uu_x=\sqrt\nu \eta(t,x), x\in S^1, \int u dx\equiv \int\eta dx\equiv0, $$ with $0<\nu\le1$ and smooth in $x$ white in $t$ random force $\eta$, we study the limiting long-time behaviour
Externí odkaz:
http://arxiv.org/abs/1002.1294
We consider the damped-driven KdV equation $$ \dot u-\nu{u_{xx}}+u_{xxx}-6uu_x=\sqrt\nu \eta(t,x), x\in S^1, \int u dx\equiv \int\eta dx\equiv0, $$ where $0<\nu\le1$ and the random process $\eta$ is smooth in $x$ and white in $t$. For any periodic fu
Externí odkaz:
http://arxiv.org/abs/0710.3869
Autor:
Eliasson, L. Hakan, Kuksin, Sergei B.
Publikováno v:
Annals of Mathematics, 2010 Jul 01. 172(1), 371-435.
Externí odkaz:
https://www.jstor.org/stable/20752272
Autor:
Kuksin, Sergei B., Bambusi, Dario
Publikováno v:
In Handbook of Dynamical Systems 2006 1 Part B:1087-1133
Autor:
Kuksin, Sergei B.
Publikováno v:
Analysis of Hamiltonian PDEs.
Externí odkaz:
https://doi.org/10.1093/oso/9780198503958.003.0004
Autor:
Kuksin, Sergei B.
Publikováno v:
Analysis of Hamiltonian PDEs.
Externí odkaz:
https://doi.org/10.1093/oso/9780198503958.003.0010