Zobrazeno 1 - 10
of 92
pro vyhledávání: '"Maspero, Alberto"'
We consider time dependently perturbed quantum harmonic oscillators in $\mathbb{R}^2$: $$ {\rm i} \partial_t u=\frac12(-\partial_{x_1}^2-\partial_{x_2}^2 + x_1^2+x_2^2)u +V(t, x, D)u, \qquad \ x \in \mathbb{R}^2, $$ where $V(t, x, D)$ is a selfadjoin
Externí odkaz:
http://arxiv.org/abs/2410.00850
Autor:
Maspero, Alberto, Murgante, Federico
We consider the problem of transfer of energy to high frequencies in a quasilinear Schr\"odinger equation with sublinear dispersion, on the one dimensional torus. We exhibit initial data undergoing finite but arbitrary large Sobolev norm explosion: t
Externí odkaz:
http://arxiv.org/abs/2408.01097
We prove the long-standing conjecture regarding the existence of infinitely many high-frequency modulational instability ``isolas" for a Stokes wave in arbitrary depth $ \mathtt{h} > 0 $, subject to longitudinal perturbations. We completely describe
Externí odkaz:
http://arxiv.org/abs/2405.05854
In this paper we consider a family of generalized Korteweg-de Vries equations and study the linear modulational instability of small amplitude traveling waves solutions. Under explicit non-degeneracy conditions on the dispersion relation, we complete
Externí odkaz:
http://arxiv.org/abs/2404.06172
We consider a modulated magnetic field, $B(t) = B_0 +\varepsilon f(\omega t)$, perpendicular to a fixed plane, where $B_0$ is constant, $\varepsilon>0$ and $f$ a periodic function on the torus ${\mathbb T}^n$. Our aim is to study classical and quantu
Externí odkaz:
http://arxiv.org/abs/2402.00428
We prove high-frequency modulational instability of small-amplitude Stokes waves in deep water under longitudinal perturbations, providing the first isola of unstable eigenvalues branching off from $\mathtt{i}\frac34$. Unlike the finite depth case th
Externí odkaz:
http://arxiv.org/abs/2401.14689
This paper fully answers a long standing open question concerning the stability/instability of pure gravity periodic traveling water waves -- called Stokes waves -- at the critical Whitham-Benjamin depth $ \mathtt{h}_{\scriptscriptstyle WB} = 1.363..
Externí odkaz:
http://arxiv.org/abs/2306.13513
We prove an almost global in time existence result of small amplitude space periodic solutions of the 1D gravity-capillary water waves equations with constant vorticity. The result holds for any value of gravity, vorticity and depth and any surface t
Externí odkaz:
http://arxiv.org/abs/2212.12255
Motivated by the problem of long time stability vs. instability of KAM tori of the Nonlinear cubic Schr\"odinger equation (NLS) on the two dimensional torus $\mathbb T^2:= (\mathbb R/2\pi \mathbb Z)^2$, we consider a quasi-periodically forced NLS equ
Externí odkaz:
http://arxiv.org/abs/2208.02040
Whitham and Benjamin predicted in 1967 that small-amplitude periodic traveling Stokes waves of the 2d-gravity water waves equations are linearly unstable with respect to long-wave perturbations, if the depth $\mathtt h$ is larger than a critical thre
Externí odkaz:
http://arxiv.org/abs/2204.00809