Explore the second lecture in a series on perturbation methods for nonlinear partial differential equations, delivered by Vishal Vasan at the International Centre for Theoretical Sciences. Delve into the application of perturbation techniques to nonlinear oscillators, focusing on finding periodic solutions. Learn about inner products, the definition of L+, perturbation series, and 2Pi periodic solutions. Gain insights into the interplay between linear waves and nonlinearity through examples from cold atoms, water waves, and atmospheric science. Conclude with a Q&A session to reinforce understanding of these advanced mathematical concepts.