Zobrazeno 1 - 10
of 130
pro vyhledávání: '"Bronski, Jared C."'
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
We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third order), the n
Externí odkaz:
http://arxiv.org/abs/2309.03962
We consider a scalar field governed by an advection-diffusion equation (or a more general evolution equation) with rapidly fluctuating, Gaussian distributed random coefficients. In the white noise limit, we derive the closed evolution equation for th
Externí odkaz:
http://arxiv.org/abs/2202.11223
We investigate the stability of traveling front solutions to nonlinear diffusive-dispersive equations of Burgers type, with a primary focus on the Korteweg-de Vries-Burgers (KdVB) equation, although our analytical findings extend more broadly. Manipu
Externí odkaz:
http://arxiv.org/abs/2112.04700
We examine the spectral stability and instability of periodic traveling waves for regularized long-wave models. Examples include the regularized Boussinesq, Benney--Luke, and Benjamin--Bona--Mahony equations. Of particular interest is a striking new
Externí odkaz:
http://arxiv.org/abs/2105.15099
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the frequency se
Externí odkaz:
http://arxiv.org/abs/2007.04343
A number of recent papers have considered signed graph Laplacians, a generalization of the classical graph Laplacian, where the edge weights are allowed to take either sign. In the classical case, where the edge weights are all positive, the Laplacia
Externí odkaz:
http://arxiv.org/abs/2005.09608
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In this paper we present a rigorous modulational stability theory for periodic traveling wave solutions to equations of nonlinear Schr\"odinger (NLS) type. We first argue that, for Hamiltonian dispersive equations with a non-singular symplectic form
Externí odkaz:
http://arxiv.org/abs/1910.05392
Beginning with the work of Lohe [14,15] there have been a number of papers [3,5,8,9,11] that have generalized the Kuramoto model for phase-locking to a non-commuting situation. Here we propose and analyze another such model. We consider a collection
Externí odkaz:
http://arxiv.org/abs/1903.09223