Lectures on nonlinear integrable equations and their solutions
Abstract
This is an introductory course on nonlinear integrable partial differential and differential-difference equ\-a\-ti\-ons based on lectures given for students of Moscow Institute of Physics and Technology and Higher School of Economics. The typical examples of Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP) and Toda lattice equations are studied in detail. We give a detailed description of the Lax representation of these equations and their hierarchies in terms of pseudo-differential or pseudo-difference operators and also of different classes of the solutions including famous soliton solutions. The formulation in terms of tau-function and Hirota bilinear differential and difference equations is also discussed. Finally, we give a representation of tau-functions as vacuum expectation values of certain operators composed of free fermions.
Cite
@article{arxiv.1812.11830,
title = {Lectures on nonlinear integrable equations and their solutions},
author = {A. Zabrodin},
journal= {arXiv preprint arXiv:1812.11830},
year = {2019}
}
Comments
92 pages