Institute for Mathematical Modelling RAS,

Miusskaya Pl. 4A, Moscow, 125047 RUSSIA

E-mail: kovalev@imamod.ru

and

Bogoliubov Lab. of Theoretical Physics,

Joint Institute for Nuclear Research,

141980 Dubna, Moscow Region, RUSSIA

E-mail: shirkovd@thsun1.jinr.ru

**The renormalization group symmetry for solution of
integral equations**

**Abstract:**

Evolution of the renormgroup algorithm and the related renormgroup
symmetry, introduced in mathematical physics for solutions of boundary-value
problems based on differential equations, is reviewed. We discuss the essential
progress made recently in the application of this algorithm to models with
integral equations. Several physical illustrations from nonlinear optics,
plasma physics, and other fields of theoretical physics demonstrate the
potentialities of the algorithm for models with nonlocal terms in the form
of the linear solution functionals.