The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science
 
                 Mathematical Analysis and Applications Seminar
 
                     Lecture Hall, Room 1, Ziskind Building
                           on Tuesday, March 29, 2011
                                  11:00 - noon
 
                                Alexander Rasin
 
                                 will speak on
 
                               The Gardner method
                   for differential and difference equations
 
Abstract:
40 years ago Gardner proposed the method for generation of infinite hierarchy
of conservation laws for integrable PDEs. We managed to extend his theory in
two directions: First of all we developed the analog of the Gardner method for
generating the symmetries of KdV and potential KdV. To do this we identify
symmetry for potential KdV which depends upon a parameter. The expansion of
this symmetry in a formal power series in the parameter gives the usual
infinite hierarchy of symmetries. The corresponding symmetry can be written for
KdV and used to construct the infinite hierarchy of symmetries for KdV.
Secondly, we present Gardner methods for generation of conservation laws and
symmetries for partial difference equations. We show that all the necessary
information for the application of the Gardner method, namely Backlund
transformations and initial conservation laws, follow from the multidimensional
consistency.
 
            Mathematical Analysis and Applications Seminar Web Page:
               <http://www.wisdom.weizmann.ac.il/~vered/analsem.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Diana Mandelik   <diana.mandelik@weizmann.ac.il>