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 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...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

In this paper, we study the existence and uniqueness of the global smooth solution for the initial value problem of generalized Zakharov equations in dimension two. By means of a priori integral estimates and Galerkin method, we first construct the existence of global solution with some conditions. Furthermore, we prove that the global solution is unique. c ©2017 All rights reserved.