The phase shift of line solitons for the KP-II equation

The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the $L^\infty$-bound for the local phase shift of modulating line solitons for polynomially localized perturbations

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at http://www.mis.mpg.de/preprints/index.html

Using viral vectors as gene transfer tools (Cell Biology and Toxicology Special Issue: ETCS-UK 1 day meeting on genetic manipulation of cells)

In recent years, the development of powerful viral gene transfer techniques has greatly facilitated the study of gene function. This review summarises some of the viral delivery systems routinely used to mediate gene transfer into cell lines, primary cell cultures and in whole animal models. The systems described were originally discussed at a 1-day European Tissue Culture Society (ETCS-UK) workshop that was held at University College London on 1st April 2009. Recombinant-deficient viral vectors (viruses that are no longer able to replicate) are used to transduce dividing and post-mitotic cells, and they have been optimised to mediate regulatable, powerful, long-term and cell-specific expression. Hence, viral systems have become very widely used, especially in the field of neurobiology. This review introduces the main categories of viral vectors, focusing on their initial development and highlighting modifications and improvements made since their introduction. In particular, the use of specific promoters to restrict expression, translational enhancers and regulatory elements to boost expression from a single virion and the development of regulatable systems is described