A.M. Kamchatnova,b aMoscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow Region, 141700, Russian Federation bInstitute of Spectroscopy, Russian Academy of Sciences, ul. Fizicheskaya 5, Troitsk, Moscow, 108840, Russian Federation
Introduction into the theory of dispersive shock waves is presented in framework of the approach formulated by Gurevich and Pitaevskii in the paper  based on the Whitham theory for modulations of nonlinear waves. The Whitham equations are derived for modulations of periodic waves in the Korteweg-de Vries equation theory and the elementary methods for finding their solutions are explained. This approach is illustrated by solutions of basic problems considered by Gurevich and Pitaevskii. Generalization of the theory to systems with weak dissipation is discussed. Exposition of the theory of dispersive shock waves for the Gross—Pitaevskii equation is given.