Zobrazeno 1 - 10
of 266
pro vyhledávání: '"37K45"'
We found two stationary solutions of the parametrically driven, damped nonlinear Schr\"odinger equation with nonlinear term proportional to $|\psi(x,t)|^{2 \kappa} \psi(x,t)$ for positive values of $\kappa$. By linearizing the equation around these e
Externí odkaz:
http://arxiv.org/abs/2411.17655
Autor:
Curran, Mitchell, Marangell, Robert
We use the Maslov index to study the eigenvalue problem arising from the linearisation about a standing wave in the fourth-order cubic nonlinear Schr\"odinger equation (NLSE). Our analysis is motivated by a recent work by Bandara et. al., in which th
Externí odkaz:
http://arxiv.org/abs/2411.16903
We study quasi-periodic eigenvalue problems that arise in the stability analysis of periodic traveling wave solutions to Hamiltonian PDEs. We establish bounds on regions in the complex plane when the eigenvalues may deviate from the imaginary axis, a
Externí odkaz:
http://arxiv.org/abs/2410.19113
Autor:
Eisenhuth, Benedikt, Grothaus, Martin
We consider a degenerate infinite dimensional stochastic Hamiltonian system with multiplicative noise and establish the essential m-dissipativity on $L^2(\mu^{\Phi})$ of the corresponding Kolmogorov (backwards) operator. Here, $\Phi$ is the potential
Externí odkaz:
http://arxiv.org/abs/2410.15993
We study the question of when a distributed port-Hamiltonian system is bounded-input bounded-output (BIBO) stable. Exploiting the particular structure of the transfer function of these systems, we derive several sufficient conditions for BIBO stabili
Externí odkaz:
http://arxiv.org/abs/2410.12697
We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.
Comment: 29 pages, 1 figure
Comment: 29 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2409.01663
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 are concerned with normalized solutions in $H_{r}^{1}(\mathbb{R}^{3}) \times H_{r}^{1}(\mathbb{R}^{3})$ for Hartree-Fock type systems with the form \be\lab{ Hartree-Fock} \left\{ \begin{array}{ll} -\Delta u +\alpha \phi _{u,v} u=\la
Externí odkaz:
http://arxiv.org/abs/2405.01036
Autor:
Pilod, Didier, Valet, Frédéric
We study the dynamics of the collision of two solitary waves for the Zakharov-Kuznetsov equation in dimension $2$ and $3$. We describe the evolution of the solution behaving as a sum of $2$-solitary waves of nearly equal speeds at time $t=-\infty$ up
Externí odkaz:
http://arxiv.org/abs/2403.02262
Autor:
Bernier, Joackim, Camps, Nicolas
We consider nonlinear Schr\"odinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of most of the
Externí odkaz:
http://arxiv.org/abs/2402.04122