In the academic year 1973-1974, Professor Martin Kruskal, of Princeton University, visited the Weizmann Institute. He delivered a series of lectures on a new method for solving certain classes of nonlinear partial differential equations based on the so-called inverse scattering transform.
The main example was the KdV (Korteweg de Vries) equation. The basic idea is to identify solutions u(x,t) of the KdV equation as the potentials of a family of Schrodinger equations in the variable x with the variable t serving to index the family. A fundamental observation is that the spectrum of the class of Schrodinger equations with potentials that evolve in accordance with the KdV equation is independent of t.
Following these lectures, a member of the Weizmann Department of Mathematics found an analogous connection between another nonlinear evolution equation and an isospectral family of string equations. Professor Kruskal discussed the newly proposed equation in subsequent lectures and named it after the Weizmann faculty member. Over the past 40 years the properties of this nonlinear evolution equation have been extensively studied by many other investigators (who sometimes refer to it as the HD equation for short).