We study the scattering theory for the Zakharov equation in three space dimensions. We show the unique existence of the solution for this equation which tends to the given free profile with no restriction on the size of the scattered states and on the support of the Fourier transform of them. This yields the existence of the pseudo wave operators.

The axial anomaly in 2 dimensional QED at finite temperature is carefully investigated in the real time formalism in the limit of vanishing fermion mass. We follow the dispersion approach of Dolgov and Zakharov. The temperature independence of the anomaly is recovered.

We prove that the van Dam-Veltman-Zakharov discontinuity arising in the massless limit of massive gravity theories is peculiar to Minkowski space and it is not present in Anti De Sitter space, where the massless limit is smooth. More generally, the massless limit is smooth whenever the square of the graviton mass vanishes faster than the cosmological constant.

In [1] a hyperbolic analogue of pseudoanalytic function theory was developed. In the present contribution we show that one of the central objects of the inverse problem method the Zakharov-Shabat system is closely related to a hyperbolic Vekua equation for which among other results a generating sequence and hence a complete system of formal powers can be constructed explicitly.

In this paper, the well-known He’s variational iteration method (VIM) is used to construct solitary wave solutions for the generalized Zakharov equation (GZE). The chosen initial solution (trial function) can be in soliton form with some unknown parameters, which can be determined in the solution procedure. c © 2007 Elsevier Ltd. All rights reserved.

In this paper an approximate analytical solution of the fractional Zakharov-Kuznetsov equations will be obtained with the help of the reduced differential transform method (RDTM). It is indicated that the solutions obtained by the RDTM are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

This paper considers the existence of the generalized solution to the initial vale problem for a generalized Zakharov equation in dimension two. By a priori integral estimates and the Galerkin method, one can arrive at the global generalized solution to the problem.