5 papers · 1 filter
Existence and stability for traveling waves of fourth order semilinear wave and Schrodinger equations
Vishnu Iyer, Ross Parker, Atanas G. Stefanov
We investigate the existence and spectral stability of traveling wave solutions for a class of fourth-order semilinear wave equations, commonly referred to as beam equations. Using…
Asymptotic attraction with algebraic rates toward fronts of dispersive-diffusive Burgers equations
Milena Stanislavova, Atanas G. Stefanov
Burgers equation is a classic model, which arises in numerous applications. At its very core it is a simple conservation law, which serves as a toy model for various dynamics pheno…
Kinks of fractional models: existence, uniqueness, monotonicity, stability, and sharp asymptotics
Atanas G. Stefanov, P. G. Kevrekidis
In the present work we construct kink solutions for different (parabolic and wave) variants of the fractional model, in both the sub-Laplacian and super-Laplacian setting. We…
Dynamics of the Drinfeld-Sokolov-Wilson system: well-posedness and (in)stability of the traveling waves
Ognyan Christov, Sevdzhan Hakkaev, Seungly Oh +1
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regulari…
Existence and stability for the travelling waves of the Benjamin equation
Sevdzhan Hakkaev, Milena Stanislavova, Atanas G. Stefanov
In the seminal work of Benjamin,\cite{Ben} in the late 70's, he has derived the ubiquitous Benjamin model, which is a reduced model in the theory of water waves. Notably, it contai…