Integrability of Klein–Gordon Equations

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.

On Integrability of Systems of Evolution Equations

have at most finitely many symmetries by using number theory. We list the nine exceptional cases when the systems do have infinitively many symmetries. For such systems, we give the recursive operators to generate their symmetries. We treat both the commutative and the noncommutative (or quantum) case. This is the first example of a class of equations where such a classification has been possible.

Integrability of Discrete Equations Modulo a Prime

We apply the “almost good reduction” (AGR) criterion, which has been introduced in our previous works, to several classes of discrete integrable equations. We verify our conjecture that AGR plays the same role for maps of the plane define over simple finite fields as the notion of the singularity confinement does. We first prove that q-discrete analogues of the Painlevé III and IV equations hav...

Preface: Symmetries and Integrability of Difference Equations

Preface: Symmetries and Integrability of Difference Equations