Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori
In this paper we prove a result of almost global existence for some abstract nonlinear PDEs
on flat tori and apply it to some concrete equations, namely a nonlinear Schrödinger …
on flat tori and apply it to some concrete equations, namely a nonlinear Schrödinger …
One dimensional energy cascades in a fractional quasilinear NLS
A Maspero, F Murgante - arXiv preprint arXiv:2408.01097, 2024 - arxiv.org
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 …
odinger equation with sublinear dispersion, on the one dimensional torus. We exhibit initial …
The Cauchy problem for the nonlinear Schr\" odinger equation with a convolution potential
A Esfahani, A Tesfahun - arXiv preprint arXiv:2404.03568, 2024 - arxiv.org
This paper investigates the nonlinear Schr\"{o} dinger equation with a singular convolution
potential. It demonstrates the local well-posedness of this equation in a modified Sobolev …
potential. It demonstrates the local well-posedness of this equation in a modified Sobolev …
Shadowing of non-transversal heteroclinic chains in lattices
A Delshams, P Zgliczynski - arXiv preprint arXiv:2406.00398, 2024 - arxiv.org
We deal with dynamical systems on complex lattices possessing chains of non-transversal
heteroclinic connections between several periodic orbits. The systems we consider are …
heteroclinic connections between several periodic orbits. The systems we consider are …