Report Title: How to transform the KP system in the form of pseudo-differential operators into

dispersionless form.

Presenter: Professor Maksim Pavlov, Lebedev Institute of Physics, Russian Academy of Sciences

Report Time: 14:30-15:30 p.m. on Friday, May 16, 2025

Report Location: Room A302, School of Mathematics

Biography of the Speaker: Professor Maksim Pavlov graduated from the Lebedev Institute of Physics of the Russian Academy of Sciences, under the tutelage of Professor S. P. Novikov, a Fields Medalist, and obtained a doctoral degree. He/She is currently a researcher at the Lebedev Institute of Physics.

Research directions: Hamiltonian structures of integrable systems, Darboux transformations, dispersion-free integrable systems, etc. The papers were published in Comm. Math. Phys., IMRN, Nonlinearity, J. Nonlinear Sci., Stud. Appl. Math., Physica D., Lett. Math. Phys. Such as periodicals. The achievements have been cited over a thousand times and have been invited to give keynote speeches at important international conferences in the field of mathematical physics on multiple occasions.

Report Summary: We shall consider KP hierarchy together with its two-dimensional reductions. Polynomial, rational and logarithmic.Then we consider their dispershionless limits.Dispershionless limits of Lax representations and Isomonodromic deformations.Also we shall discuss hydrodynamic chains. Benney moment chain and Kupershmidt chains.Their relationships with three-dimensional quasilinear systems of first order.