Laboratory of Particle Physics,

Joint Institute for Nuclear Research,

141980 Dubna, Moscow Region, RUSSIA

E-MAIL: savina@thsun1.jinr.ru

**On a correspondence between N = 2 mKdV and N
= 2 sin-Gordon equations**

**Abstract:**

The correspondence between mKdV and sin-Gordon equations for the *N*
= 2 case is considered. By analogy with a nonsupersymmetric case it is
established that the sin-Gordon equation coincides with the first negative
flow of mKdV hierarchy realized in the ciral basis. Inverse recursion operators
are calculated for two values of parameter "*a*" labelling the mKdV
hierarchy, for the case of *a* = 4 and *a* = -2.