#### Milestone Year

### 1974

#### A new class of isospectral problems

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).