Perturbation Theories and Nonlinear Waves

This book gives an introduction to the perturbation theory for nonlinear waves in dispersive and dissipative media. The popular integrable evolution equations are generalized to include effects of dissipation, inhomogeneity, and media rotation, among others. Non-integrable model equations are also considered. A systematic description of the perturbation method based on the Lagrangian approach is developed in application to solitons, kinks, shock waves, and vortices. Moreover, the interaction of solitary waves in terms of interacting classical particles is presented. All of these basic theoretical ideas are illustrated by many practical examples throughout the book.