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Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that…
A new type of exact solvability is reported. We study the general central polynomial potentials (with 2q anharmonic terms) which satisfy the Magyari's partial exact solvability conditions (this means that they possess a…
We study the radial relaxation dynamics toward equilibrium and time-periodic pulsating spherically symmetric gas bubbles in an incompressible liquid due to thermal effects. The asymptotic model ([A. Prosperetti, J. Fluid Mech., 1991] and…
This work continues to study the set of quasi exactly solvable potentials related to the Eckart, Hult\'{e}n, Rosen-Morse, Coulomb and the harmonic oscillator potentials. We solve the Schr\"{o}dinger equation for each potential and obtain…
The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the Levi-Civita…
Laminar flows through pipes driven at steady, pulsatile or oscillatory rates undergo a sub-critical transition to turbulence. We carry out an extensive linear non-modal stability analysis of these flows and show that for sufficiently high…
There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean…
We introduce the harmonic oscillator on the Lobachevsky plane with the aid of the potential $V(r)=(a^2\omega^2/4)sinh(r/a)^2$ where $a$ is the curvature radius and $r$ is the geodesic distance from a fixed center. Thus the potential is…
The Dunkl Laplacian is used to define the Hamiltonian of a modified quantum harmonic oscillator, associated with any finite reflection group. The potential is a sum of the inverse squares of the linear functions whose zero sets are the…
In this paper, the $d$-dimensional quantum harmonic oscillator with a pseudo-differential time quasi-periodic perturbation \begin{equation}\label{0} \text{i}\dot{\psi}=(-\Delta+V(x)+\epsilon W(\omega t,x,-\text{i}\nabla))\psi,\ \ \ \ \…
A new family of one-dimensional quantum models is proposed in terms of new potentials with a Gaussian asymptotic behavior but approaching to the potential of the harmonic o scillator when $x\to 0$. It is shown that, in the energy basis of…
Interactions between fluids and elastic solids are ubiquitous in application ranging from aeronautical and civil engineering to physiological flows. Here we study the pulsatile flow through a two-dimensional Starling resistor as a simple…
In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational…
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. In this article the first- and second- order supersymmetric transformations will be used to obtain new…
We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the…
The spatio-temporal dynamics of separation bubbles induced to form in a fully-developed turbulent boundary layer (with Reynolds number based on momentum thickness of the boundary layer of 490) over a flat plate are studied via direct…
We complement the low-energy gravi-dilaton effective action of string theory with a non-local, general-covariant dilaton potential, and obtain homogeneous solutions describing a non-singular (bouncing-curvature) cosmology. We then compute,…
First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime.…
We study nonlinear dynamics in a model of three interacting encapsulated gas bubbles in a liquid. The model is a system of three coupled nonlinear oscillators with an external periodic force. Such bubbles have numerous applications, for…
Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which…