Nineteen vortex equations and integrability

INTEGRABILITY OF CHERN-SIMONS-HIGGS VORTEX EQUATIONS and A REDUCTION OF THE SELF-DUAL YANG-MILLS EQUATIONS TO THREE DIMENSIONS

I would like to make brief presentations on two topics, both of which focus on an issue of ‘integrability’ in equations of interest in high energy physics. In my first talk, I would like to introduce the Chern-Simons-Higgs vortex equations, which describe classical solutions of a certain (2+1)-dimensional field theory. In flat spacetime these equations are non-integrable, but in curved spacetim...

Integrability of Klein - Gordon Equations *

Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

Preface: Symmetries and Integrability of Difference Equations

Preface: Symmetries and Integrability of Difference Equations

Integrability of Riccati equations and the stationary KdV equations

Using the S.Lie’s infinitesimal approach we establish the connection between integrability of a one-parameter family of the Riccati equations and the stationary KdV hierarchy. In this paper we will suggest a method for integrating a one-parameter family of the Riccati equations ux + u 2 = f(x, λ) (1) based on their Lie symmetries. Here f(x, λ) = λ + λVn−1(x) + · · ·+ λV1(x) + V0(x) and λ is an ...