Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation

Existence of solutions of a kinetic equation

A global existence theorem is presented for a kinetic problem of the form @ t f + v r x f = Q(f) ; f (t = 0) = f 0 ; where Q(f) is a simpliied model wave-particle collision operator extracted from quasi-linear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f. Therefore, the assumptions on the data are such that vacuum regions, where the mean...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Existence of Solutions of a Kinetic Equation Modelling Cometary Flows

A global existence theorem is presented for a kinetic problem of the form ∂tf + v · ∇xf = Q(f) , f(t = 0) = f0 , where Q(f) is a simplified model wave-particle collision operator extracted from quasilinear plasma physics. Evaluation of Q(f) requires the computation of the mean velocity of the distribution f . Therefore, the assumptions on the data are such that vacuum regions, where the mean ve...

Nonlocal kinetic equation : integrable hydrodynamic reductions , symmetries and exact solutions

By Gennady A. El†, Anatoly M. Kamchatnov‡, Maxim V. Pavlov z and Sergey A. Zykov § † Department of Mathematical Sciences, Loughborough University, Loughborough, UK ‡Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, Russia z Lebedev Physical Institute, Russian Academy of Sciences, Moscow § SISSA, Trieste, Italy, and Institute of Metal Physics, Urals Division of Russ...

Analytical solutions for the fractional Fisher's equation

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...