8 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 $(-Î)…
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. W…