Formal and analytic solutions of differential, difference and discrete equations

Formal and Analytic Solutions of Differential, Difference and Discrete Equations

25.08.2013 -  31.08.2013 | Będlewo

Announcements

Deadline for registration: May 31, 2013

For more details about the conference visit also the webpage: http://www.impan.pl/~fasde

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Conference poster (PDF)

The theory of differential, difference and discrete equations in the complex plane is very rich. Many models of mathematical physics can be described by differential or difference equations (or integrable systems) and it is desirable to describe their solutions and their singularities, which often are related to critical phenomena. Most of the well-known special functions of mathematical physics solve differential/difference equations.

The methods of resurgent functions and multisummability, invented by J. Ecalle in 80's, have become powerful tools for solving ordinary differential and difference equations. It is generally expected that these methods can be applied to the study of PDEs. In fact, a considerable progress has been made in that direction during the last few years. On the other hand, the theory of summability of formal solutions to (partial) difference equations has just started to develop.

The goal of the conference is to bring together the leading experts in differential/difference equations, special functions, orthogonal polynomials, asymptotic analysis of ODEs/PDEs, especially those related to mathematical physics. The meeting is expected to be an excellent opportunity to exchange the most recent results and to coordinate future research as well as to promote existing and start new collaboration between colleagues in different countries.

Similar meetings, which took place in Będlewo in 2008 and 2011, gathered 31 and 44 participants, respectively, and new international collaborations between the participants started. We expect this time there will be a similar number of participants and the conference will strengthen the cooperation between them.

Main topics:

  • Ordinary differential equations in the complex plane. Formal and analytic solutions. Stokes multipliers.
  • Difference and discrete equations, including the q-cases. Dynamic equations.
  • Special functions (hypergeometric functions and others), orthogonal polynomials, continuous and discrete Painlevé equations.
  • Formal solutions of PDEs (heat, semilinear heat, Burgers type, KdV, nonlinear Schrödinger).
  • Holomorphic vector fields. Normal forms.
  • Summability of WKB solutions, singular perturbations problems.
  • Asymptotic expansions, Borel summability, Gevrey estimates. Summability of formal solutions of difference equations.
  • Integrable systems.
  • Applications in applied mathematics and mathematical physics.

 

 

 

 

 

 

 

 

The conference is co-financed by:
Warsaw Center of Mathematics and Computer Science