Seminar

In this talk, we discuss the inverse scattering theory in the context of the KdV equation. The KdV equation describes non-dissipative nonlinear dispersive waves in one dimension and arose in the context of solitary waves in shallow water. We discuss the Hamiltonian-Poisson bracket formulation and Lax pairs for the KdV equation. We show how the existence of the Lax pairs simplifies the nonlinear problem. Then we explain the step-by-step process in the inverse scattering to solve the KdV initial value problem. Finally, we explicitly obtain the one-soliton solution of the KdV equation using inverse scattering theory.