The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations sh...

For various spaces of potentials we prove that the set of finite gap potentials of the ZakharovShabat system is dense. In particular our result holds for Sobolev spaces and for spaces of analytic potentials of a given type. Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-21875 Originally published at: Grébert, B; Kappeler, T (2003). D...

In this paper we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results and the behavior of higher order Sobolev norms of the solutions. Smoothing means that the nonlinear part of the solution on the half line is smoother than the initial...

Consider the 2 × 2 first order system due to Zakharov-Shabat,

In this paper we investigate the existence of soliton solutions for a modified form of the Zakharov equations describing modulational instabilities in quantum plasmas. In particular, we show that quantum effects suppress the easily identifiable soliton solutions, obtained in the adiabatic limit. In this limit, the quantum Zakharov equations become a coupled fourth order system, not amenable to ...

In this paper, a singularity structure analysis of the (2+1)-dimensional Zakharov equation is carried out and it is shown that it admits the Painleve property. The bilinear form of this equation is derived from the Painleve analysis in a straightforward manner. Using this bilinear form, we have constructed the simply one soliton solution by the Hirota method. We have then presented the localize...