Abstract
We define the notion of Darboux integrability for linear second order partial differential operators,.We then build on certain geometric results of E. Vessiot related to the theory of Monge characteristics to show that the Darboux integrable operators L can be used to obtain a solution of the A2 Toda field theory. This solution is parametrised by four arbitrary functions. The approach presented in this paper thereby represents an alternative means of linearising the A2 Toda equations and may be contrasted with the known linearisation via the Lax pair.
Publisher
Cambridge University Press (CUP)
Reference13 articles.
1. Sur les equations aux derives partielles du second ordre F(x, y, z, p, q, r, s, t) = 0 integrable par la methode de Darboux;Vessiot;J. Math. Pures Appl.,1939
2. [11] Vassiliou P.J. , in preparation.
3. Representation of zero curvature for the system of nonlinear partial differential equations $$x_{\alpha ,z\bar z} = \exp (kx)_\alpha $$ and its integrability
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. The multidimensional Darboux transformation;Journal of Geometry and Physics;1998-07