In this article, we use the general theory derived in Paper I [M. Tacu and D. Bénisti, Phys. Plasmas 29, 052108 (2022)] order to address several long-standing issues regarding nonlinear electron plasma waves (EPWs). First, discuss relevance practical usefulness of stationary solutions Vlasov–Poisson system, so-called Bernstein–Greene–Kruskal modes, model slowly varying waves. Second, derive an ...