Study on the behavior of solutions in the zero dispersion limit of the nonlinear wave equations with the integral kernel

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1. Exactly solvable eigenvalue problemThe linear eigenvalue problem is solved for the nonlocal nolonear Schrodinger (NLS) equation in the context of the inverse scattering method when the potential is the multisolison solution2. Relation to exactly solvable dynamical systemsThe motion of poles of the soliton and periodic solutions of the nonlocal NLS equation is investigated from the viewpoint of the dynamical system in the complex plane3. Modulation theoryThe modulation problem is analyzed for the periodic solution of the nonlocal NLS equation. The modulation equations for the wave parameters are derived and they are solved explicitly4. Formulation of the initial value problemThe initial value problem of the nonlocal NLS equation is formulated by means of the inverse scattering transform method. A system of equations are derived for the Jost functions5. New formula for the soliton solutionThe multisoliton solution of the Benjamin-Ono equation is derived from a system of nonlinear algebraic equations. This result is a new finding which is never anticipated from the scheme of the inverse scattering method