Selection of real regular finite gap-solutions of soliton equations - II

Lecture 2: “Difficult case” 1. Focusing Nonlinear Schr¨odinger equation. Cherednik differential for the Nonlinear Schr¨odinger equation. Characterization of divisors for real solutions in terms of Cherednik differential. Elementary characterization of admissible divisors. Regularity of all real solutions. 2. Sine-Gordon equation. Cherednik differential for the Since-Gordon equation. Characterization of divisors for real solutions in terms of Cherednik differential. Elementary characterization of admissible divisors. Regularity of all real solutions. 3. Number of connected components in the space of solutions for a fixed spectral curve. 4. Real regular Kadomtsev-Perviashvili I solutions.