Linear waves Group velocity, dispersion Geometrical optics Linear Korteveg-de Vrise equation and its exact solution Some examples: plasma ion sound, shallow water waves Simple waves Umklapp Method of characteristics Weak shock waves Simple waves in gas dynamics Burgers equation, Cole-Hopf substitution General solution, area rule Korteveg-de Vrise equation Conidal waves, solitons Conservation laws Miura substitution Inverse scattering problem for Korteveg-de Vrise equation N-soliton solution, "tails" Lax representation Conservation laws as the consequence of transmission amplitude invariance Hamiltonian form of Korteveg-de Vrise equation Integrability of Korteveg-de Vrise equation in the classical sense sine-Gordon, non-linear Schrodinger equations Soliton solution Consistency requirement for U and V operators Matrix operators for Korteveg-de Vrise, sine-Gordon and NS equations Scattering matrix Inverse scattering problem technique Witham averaging technique Nonlinear Klein-Gordon equation Riemann invariants Backlund transformation Hirota transformation Connection between Backlund transformation and inverse scattering problem Nonlinear optics Nonlinear parabolic equation Self-modulation, focusing instability Lighthill condition Self-focusing, collapse Nonlinear phases of "classical" instabilities Kelvin-Helmholtz and Taylor instabilities Nonlinear phase Bunemann and beam instability   LITERATURE: V.I. Karpman Nonlinear Waves in Dispersive Media J. Witham Linear and Nonlinear Waves P. Bhatnagar Nonlinear Waves in One-dimensional Dispersion Systems V.Ye. Zakharov, S.V. Manakov, S.P. Novikov, L.P. Pitaevsky. Theory of Solitons and Inverse Problem Technique