Related papers: Pole dynamics for the Flierl-Petviashvili equation…
We propose a new phenomenology of the generation of internal transport barriers, based on the exact periodic solution of the Flierl-Petvishvili equation. We examine the stability of this solution and compare the late stages of the flow with…
The interaction between planetary waves and an arbitrary zonal flow is studied from a phase-space viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the…
Using variational methods, we construct approximate solutions for the Gross-Pitaevski equation which concentrate on circles in $\R^3$. These solutions will help to show that the $L^2$ flow is unstable for the usual topology and for the…
In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schr\"{o}dinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the…
In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space $W^1L^{\Phi}([0,T])$. We employ the direct method of calculus of variations and we consider a potential function $F$…
Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally…
The real, nonsingular elliptic solutions of the Korteweg-deVries equation are studied through the time dynamics of their poles in the complex plane. The dynamics of these poles is governed by a dynamical system with a constraint. This…
Exploring the general analytical solutions to the Euler equations for ideal fluids holds significant theoretical and practical importance. The steady flows in two-dimensional spaces are considered whether there is an analytical solution in…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
A new, frequency modulation mechanism for zonal flow pattern formation is presented. The model predicts the probability distribution function of the flow strength as well as the evolution of the characteristic spatial scale. Magnetic…
In this paper, we obtain the existence result of smooth solutions to the Orlicz-Aleksandrov problem from the perspective of geometric flow. Furthermore, a special uniqueness result of solutions to this problem shall be discussed.
An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting…
The self-organization of turbulence into regular zonal flows can be fruitfully investigated with quasilinear methods and statistical descriptions. A wave kinetic equation that assumes asymptotically large-scale zonal flows is pathological.…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
The conformal mapping approach is a well established technique for solving the Euler equations for potential flows with one spatial dimension. In this work, we extend this framework to problems with a weakly transversal dependence and, by…
We study the dynamics of roots of f'(z,t), where f(z,t) is a locally univalent polynomial solution of the Polubarinova-Galin equation for the evolution of the conformal map onto a Hele-Shaw blob subject to injection at one point. We give…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
The paper considers dynamics in the Charney-Hasegawa-Mima equation, basic to several different phenomena. In each of them, the generation of poloidal/zonal flow is important. The paper suggests a possibility to generate such flows (which…