: A famous transformation that maps the nonlinear viscous Burgers' equation to the linear heat equation. Hodograph and Legendre Transforms
: Typically applied to time-dependent problems on semi-infinite intervals. Converting Nonlinear into Linear PDEs Cole-Hopf Transform evans pde solutions chapter 4
: Modeling solutions that move with constant speed, such as solitons in the KdV equation or traveling waves in viscous conservation laws. Scaling Invariance : Finding solutions of the form : A famous transformation that maps the nonlinear
: Evans applies this method to reaction-diffusion systems to demonstrate how spatial patterns can emerge from stable systems. Similarity Solutions evans pde solutions chapter 4