This book addresses complex issues such as the existence of homoclinic orbits and the study of chaotic behavior arising from these orbits in various perturbed nonlinear equations, including the Schrödinger equation, the Sine-Gordon equation, and the Korteweg-de Vries (KdV) equation. It provides a detailed and rigorous examination of these topics, supported by rich documentation and illustrative examples. The content reflects fundamental concepts and significant advancements in nearly integrable dynamical systems. Designed to facilitate the rapid entry of senior university students, graduate students, postdoctoral fellows, and early-career academics into the field, this book also serves as a valuable reference for researchers and educators in traditional natural sciences and engineering, aiding in the expansion of their knowledge base.