Summary
International Symposium on Nonlinear Theory and Its Applications
2016
Session Number:C2L-D
Session:
Number:C2L-D-2
Generalised Weierstrass Elliptic Functions and Nonlinear Wave Equations
Chris Eilbeck,
pp.-
Publication Date:2016/11/27
Online ISSN:2188-5079
Summary:
The well-known Weierstrass elliptic functions are constructed from an algebraic curve of genus g = 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 PDEs, such as the KdV equation (g = 2), the Boussinesq equation (g = 3), and the Kadomtsev-Petviashvili (KP) equation (g = 6). We review, very briefly, some of the results in this area.