Abstract booklet for Nonlinear Physics: Theory and Experiment. III
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booklet for Nonlinear Physics: Theory and Experiment. III Gallipoli (Lecce, Italy) 24 June – 3 July 2004 Information received within June 15, 2004 —————————————————————————————Mark J. Ablowitz Department of Applied Mathematics, University of Colorado UCB 526, Boulder 80309 CO Chazy-Darboux-Halphen Systems At the turn of the last century Painlevé and his school obtained a class of ordinary differential equations in the complex (time) plane which have no movable branch points. The second order ODEs they found include elliptic functions and the now well known six Painlevé equations. Chazy (1909) studied third order ODEs and found examples whose solutions are analytic inside/outside a circle which consists of a natural boundary of singular points. In this lecture we will show that the general solution can be written in terms of modular functions and we will discuss connections between the Chazy equation and a system of equations studied by Darboux-Halphen (1878) a generalized 9th order system, the generalized Chazy equation and the self-dual Yang-Mills equations. Remarkably the Chazy equation will be also shown to correspond to a system of equations studied by Ramanujan in 1916! —————————————————————————————Cory Ahrens Department of Applied Mathematics, University of Colorado UCB 526, Boulder 80309 CO Reduction of collision-induced timing shifts in dispersion-managed, quasi-linear systems with periodic-group-delay dispersion compensation I will first present a brief history of the development of optical communication, providing motivation for considering the current problem. Next, the basic
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تاریخ انتشار 2004