Almost periodic solutions of one dimensional nonlinear Schrödinger equation with the constant potential

Key Points

• To prove the existence of a family of almost periodic solutions for the nonlinear Schrödinger equation under constant potential.
• Analyzed frequency drift and strong Diophantine conditions.
• Utilized an improved infinite-dimensional KAM theory.
• Considered periodic boundary conditions in one dimension.
• Established the existence of small amplitude, time quasi-periodic solutions.
• The solutions lie primarily in a sparse admissible set rather than the maximum torus.