Roald Zinnurovich Sagdeev (on his 90th birthday), Aganbegyan A.G., Vainshtein A.I., Dudnikova G.I., Zakharov V.E., Zelenyi L.M., Kuznetsov E.A., Litvak Nigmatulin R.I., Ryutov D.D., Skrinskii A.N., Sunyaev R.A., Fedoruk M.P.

Aleksandr Abramovich Belevin (on his 80th birthday), Arseev P.I., Vasil’ev M.A., Vysotskii M.I., Gorskii A.S., Drinfeld V.G., Zamolodchikov A.B., Zakharov V.E., Litvinov A.V., Polyakov A.M., Rubakov V.A., Feigin B.L., Shifman M.A.

Spatial regularity properties of certain global-in-time solutions of the Zakharov system are established. In particular, the evolving solution u(t) is shown to satisfy an estimate ‖u(t)‖ Hs ≤ C|t|, where H is the standard spatial Sobolev norm. The proof is an adaptation of earlier work on the nonlinear Schrödinger equation which reduces matters to bilinear estimates.

In this paper we present approximate analytical solution of a time-fractional Zakharov-Kuznetsov equation via the fractional iteration method. The fractional derivatives are described in the Caputo sense. The approximate results show that the fractional iteration method is a very efficient technique to handle fractional partial differential equations.

In this article we show that the large time asymptotics for the Grinevich–Zakharov rational solutions of the Novikov–Veselov equation at positive energy (an analog of KdV in 2 + 1 dimensions) is given by a finite sum of localized travel waves (solitons).

Equation Vladimir Zakharov, Donald Resio, and Andrei Pushkarev Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA Lebedev Physical Institute RAS, Leninsky 53, Moscow 119991, Russia Novosibirsk State University, Novosibirsk, 630090, Russia Waves and Solitons LLC, 1719 W. Marlette Ave., Phoenix, AZ 85015, USA Taylor Engineering Research Institute, University of North Florida ...

The new ZRP wind input source term (Zakharov et al., 2012) is examined for its theoretical consistency via numerical simulation of the Hasselmann equation. The results are compared to field experimental data, collected at different sites around the world, and theoretical predictions based on self-similarity analysis. Consistent results are obtained for both limited fetch and duration limited st...