  This paper presents the final physics design of the Proton Improvement
Plan-II (PIP-II) at Fermilab, focusing on the linear accelerator (Linac) and
its beam transfer line. We address the challenges in longitudinal and
transverse lattice design, specifically targeting collective effects,
parametric resonances, and space charge nonlinearities that impact beam
stability and emittance control. The strategies implemented effectively
mitigate space charge complexities, resulting in significant improvements in
beam quality -- evidenced by reduced emittance growth, lower beam halo,
decreased loss, and better energy spread management. This comprehensive study
is pivotal for the PIP-II project's success, providing valuable insights and
approaches for future accelerator designs, especially in managing
nonlinearities and enhancing beam dynamics.
