ISRMT Seminar: Long-Time Asymptotics of Solutions to the Kadomtsev-Petviashvili I Equation

We establish the long-time asymptotics for solutions of the Kadomtsev-Petviashvili I (KP I) equation (u_t+6uu_x+u_{xxx})_x = 3 u_{yy} with small initial data, using the inverse scattering transform formalism developed by Zhou. Within this framework, the inverse problem for the KP I equation is formulated as a nonlocal Riemann-Hilbert problem (RHP) in two dimensions. As part of the asymptotic analysis, we also determine the long-time behavior of the solution to the nonlocal RHP, along with its x-derivative.