Seminario de investigación: SOLVABILITY OF INTEGRABLE PARTIAL DIFFERENTIAL EQUATIONS UNDER MEROMORPHIC INITIAL CONDITIONS BY QUADRATURE, por Kazuyuki Yagasaki

El jueves 21 de marzo de 2024 a las 12:30 h tendrá lugar el seminario de investigación titulado “Solvability of integrable partial differential equations under meromorphic initial conditions by quadrature”, impartido por Kazuyuki Yagasaki, de la Universidad de Kioto (Japón). El seminario será presencial y se impartirá en la Sala de Grados Sala F (S1.S2) de la E.T.S. de Edificación. Os animamos a todos a asistir.

ABSTRACT: I talk about my recent results on the solvability of representative integrable partial differential equations including the Korteweg-de Vries (KdV) equation and nonlinear Schrödinger equation under meromorphic initial conditions by quadrature, when the inverse scattering transform (IST) is applied. It is a key to solve the Schrödinger equation or two-dimensional Zakharov-Shabat systems appearing in the Lax pair in application of the IST. We can prove that these linear systems are always integrable in the sense of differential Galois theory if and only if the meromporphic potentials corresponding to initial condition are reflectionless, under the condition that they are absolutely integrable on R \ (−R_0, R_0) for some R_0 > 0. We will mainly concentrate on the case of the KdV equation from time constraints.