Explore perturbation methods for nonlinear PDEs in this comprehensive lecture by Vishal Vasan at the International Centre for Theoretical Sciences. Delve into the third installment of a four-part series, focusing on adapting linear equation techniques to nonlinear contexts. Learn about perturbation methods, multiple scales, and asymptotic analysis through examples from cold atoms, water waves, and atmospheric science. Gain insights into the interplay between linear waves and nonlinearity, with topics covering periodic solutions, linear operators, null-space, eigenvectors, adjoint operators, perturbation series, and more. Engage with a Q&A session and discover how to approach non-linear PDEs using these advanced mathematical techniques.