MATH 520 Mathematical Models of Nonlinear Waves

Linear hyperbolic equations and Green's functions. Linear dispersive waves and grup velocity. First order nonlinear partial differential equations; discontinuous solutions and shock waves. Linear and nonlinear diffusion equations. Burgers equation and Cole-Hopf transform. Solitary waves and solitons. KdV equation, nonlinear Schrödinger equation, Klein-Gordon and Sine-Gordon equations. Solution methods.