Exact Solutions to Nonlinear Partial Difference Equations: the Discrete KdV Equation

Ying Shi

Friday 18th October, 2013 16:00-17:00 Maths 516


Getting explicit solutions of nonlinear partial differential/difference equations (PDEs or PΔEs) is
usually a difficult task. Only in certain special cases can the solutions be written down explicitly.
However, in the theory of continuous/discrete integrable systems, for many PDEs and PΔEs (or say,
soliton equations), people have found quite a few methods, such as the inverse scattering transform,
Darboux/Bäcklund transformations, Hirota’s bilinear method, etc. to get explicit solutions. In
this talk I am going to deal with the nonlinear PΔE called the discrete KdV equation. By using the Darboux transformation, its exact solutions can be expressed as Casorati determinants.

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