9 citations · 9 across the 8 of their papers we have counts for
10 papers
Asymptotic stability for monotone traveling kinks of the dissipative Boussinesq problem
Atanas G. Stefanov
We study the dissipative Boussinesq problem, which extends the "good" Boussinesq equation by incorporating viscosity effects. It is well-known that this model supports monotone dec…
Global regularity of the 2D fractional Boussinesq equations with subcritical dissipation
Atanas Stefanov, Jiahong Wu, Xiaojing Xu +1
This paper studies the global regularity problem for the two-dimensional incompressible Boussinesq equations with fractional dissipation given by and $(-Δ)^{…
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…
On a Klein-Gordon Reduction for Oscillons
A. G. Stefanov, M. Stanislavova, J. Cuevas-Maraver +1
In the present work we examine the dynamics of a model for oscillons in 1-dimensional spacetime field theories with a cubic nonlinearity. We utilize a reduction of the model to fir…
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…
Solitary waves for the power degenerate NLS -- existence and stability
Vishnu Iyer, Atanas G. Stefanov
We consider a semilinear Schrödinger equation, driven by the power degenerate second order differential operator . We construct the solit…
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…
Smoothing - Strichartz Estimates for the Schrodinger Equation with small Magnetic Potential
Vladimir Georgiev, Atanas Stefanov, Mirko Tarulli
The work treats smoothing and dispersive properties of solutions to the Schrodinger equation with magnetic potential. Under suitable smallness assumption on the potential involving…