The additional chapters of partial differential equations Lecture 1. Introduction Lecturer: S.V. Revina The additional chapters of partial differential equations

Soliton is the solitary wave that maintains its shape while it travels at constant speed

John Scott Russell and the Union Canal, 1834

Netherlands, 1895 Korteweg - de Vriez equation

Fermi, Pasta, Ulam,1952

M.Kruskal, N.Zabusky Phys. Rev. Lett. 15, 240–243 Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States N. J. Zabusky Bell Telephone Laboratories, Whippany, New Jersey M. D. Kruskal Princeton University Plasma Physics Laboratory, Princeton, New Jersey Received 3 May 1965 © 1965 The American Physical Society

Recreation of Russell’s soliton in 1995

Fibre optic

I do not know what I may appear to the world, but to myself I seem to have been only a boy playing on the sea-shore,… whilst the great ocean of truth lay all undiscovered before me Newton, Isaak