Generalised Weierstrass elliptic functions, nonlinear wave equations, and heat equations.

Chris Eilbeck (Heriot Watt University)

Thursday 16th February, 2017 16:00-17:00 Maths 522


The well-known Weierstrass elliptic functions are constructed from an algebraic curve of genus 1, and can be used to solve a number of nonlinear ordinary differential equations, such as the travelling wave problem for the KdV equation.  As well as the soliton solution, such methods give periodic solutions of the ODEs.  If the curve is generalised to a higher genus, the corresponding generalised Weierstrass functions give multiple periodic solutions of many well-known nonlinear PDEs, such as KdV, Boussinesq and KP.  Recent work centres on associated sets of linear heat equations which can be used to form recurrence relations for the generalised Weierstrass sigma function.

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