Nonlinear wave equations. Principles of wave propagation in linear systems: dispersion. Principles of wave propagation in the presence of nonlinearity: selfaction. Stationary waves, solitons; stable balance between linear and nonlinear effects. Concept of stability and bifurcations: modulation instability. Pattern formation. Turbulence. Nonlinear wave equations and nonlinear effects in versatile physical systems. Nonlinear Schrodinger equation (NLSE): nonlinear optics, BoseEinstein condensates (BECs) (GrossPitaevskii equation). Korteweg de Vries equation (KdV): long wavelength approximation for waves in shallow water, acoustic ion waves. SineGordon equation (SG): mechanical oscillators, quantum optics. Methods for solving nonlinear wave equations: numerical simulations, inverse scattering method.

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