RARE "Theory of Solitons" Martin Kruskal Hand Signed Album Page for Sale

RARE "Theory of Solitons" Martin Kruskal Hand Signed Album Page For Sale

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RARE "Theory of Solitons" Martin Kruskal Hand Signed Album Page:
$349.99

Up for sale a RARE! the "Theory of Solitons" Martin Kruskal Hand Signed Album Page Dated 1983.

ES-7556E

Martin

David Kruskal (/ˈkrʌskəl/; September 28, 1925 – December 26, 2006) was an He made fundamental contributions in many areas of

mathematics and science, ranging from plasma physics to general relativity and

from nonlinear analysis to asymptotic analysis. His most celebrated

contribution was in the theory of solitons.

He was a student at the University of Chicago and at New York University, where

he completed his Ph.D. under Richard

Courant in 1952. He spent much of his career at Princeton University, as a

research scientist at the Plasma Physics Laboratory starting in 1951, and then

as a professor of astronomy (1961), founder and chair of the Program in Applied

and Computational Mathematics (1968), and professor of mathematics (1979). He

retired from Princeton University in

1989 and joined the mathematics department of Rutgers University,

holding the David Hilbert Chair of Mathematics. Apart from his research,

Kruskal was known as a mentor of younger scientists. He worked tirelessly and

always aimed not just to prove a result but to understand it thoroughly. And he

was notable for his playfulness. He invented the Kruskal Count, a magical effect that has been known to perplex

professional magicians because – as he liked to say – it was based not on

sleight of hand but on a mathematical phenomenon. Martin Kruskal's scientific

interests covered a wide range of topics in pure mathematics and applications

of mathematics to the sciences. He had lifelong interests in many topics in

partial differential equations and nonlinear analysis and developed fundamental

ideas about asymptotic expansions, adiabatic invariants, and numerous related

topics. His Ph.D. dissertation, written under the direction of Richard Courant and Bernard Friedman at New York University, was

on the topic "The Bridge Theorem For Minimal Surfaces." He received

his Ph.D. in 1952. In the 1950s and early 1960s, he worked largely on plasma

physics, developing many ideas that are now fundamental in the field. His

theory of adiabatic invariants was important in fusion research. Important

concepts of plasma physics that bear his name include modes. With I. B. Bernstein, E. A. Frieman, and R. M. Kulsrud,

he developed the MHD (or magnetohydrodynamic) Energy Principle. His interests extended to plasma

astrophysics as well as laboratory plasmas. Martin Kruskal's work in plasma

physics is considered by some to be his most outstanding. In 1960, Kruskal

discovered the full classical spacetime structure of the simplest type of black

hole in General Relativity. A spherically symmetric black hole can be described

by the Schwarzschild solution, which was discovered in the early days of

General Relativity. However, in its original form, this solution only describes

the region exterior to the horizon of the black hole. Kruskal (in parallel

with George Szekeres)

discovered the maximal analytic continuation of the Schwarzschild solution,

which he exhibited elegantly using what are now This led Kruskal to the astonishing discovery that the

interior of the black hole looks like a "wormhole" connecting two identical, asymptotically flat

universes. This was the first real example of a wormhole solution in General

Relativity. The wormhole collapses to a singularity before any observer or

signal can travel from one universe to the other. This is now believed to be the

general fate of wormholes in General Relativity. In the 1970s, when the thermal

nature of black hole physics was discovered, the wormhole property of the

Schwarzschild solution turned out to be an important ingredient. Nowadays, it

is considered a fundamental clue in attempts to understand quantum gravity. Kruskal's most widely known work was the

discovery in the 1960s of the integrability of certain nonlinear partial differential

equations involving functions of one spatial variable as well as time. These

developments began with a pioneering computer simulation by Kruskal and Norman Zabusky (with some assistance from Harry Dym) of a nonlinear equation known as the Korteweg–de Vries equation (KdV).

The KdV equation is an asymptotic model of the propagation of nonlinear dispersive waves. But

Kruskal and Zabusky made the startling discovery of a "solitary wave"

solution of the KdV equation that propagates nondispersively and even regains

its shape after a collision with other such waves. Because of the particle-like

properties of such a wave, they named it a "soliton," a term that caught on almost immediately. This

work was partly motivated by the near-recurrence paradox

that had been observed in a very early computer simulation of a nonlinear lattice by Enrico Fermi, John

Pasta, and Stanislaw Ulam, at Los Alamos in 1955. Those authors had observed

long-time nearly recurrent behavior of a one-dimensional chain of anharmonic

oscillators, in contrast to the rapid thermalization that had been expected.

Kruskal and Zabusky simulated the KdV equation, which Kruskal had obtained as a

continuum limit of that one-dimensional chain, and found solitonic behavior,

which is the opposite of thermalization. That turned out to be the heart of the

phenomenon. Solitary wave phenomena had been a 19th-century mystery dating back

to work by John Scott Russell who,

in 1834, observed what we now call a soliton, propagating in a canal, and

chased it on horseback. In spite of his observations of solitons in

wave tank experiments, Scott Russell never recognized them as such, because of

his focus on the "great wave of translation," the largest amplitude

solitary wave. His experimental observations, presented in his Report on Waves

to the British Association for the Advancement of Science in 1844, were viewed

with skepticism by George Airy and George Stokes because

their linear water wave theories were unable to explain them. Joseph Boussinesq (1871) and Lord Rayleigh (1876) published mathematical theories

justifying Scott Russell's observations. In 1895, Diederik Korteweg and Gustav de Vries formulated the KdV equation to describe

shallow water waves (such as the waves in the canal observed by Russell), but

the essential properties of this equation were not understood until the work of

Kruskal and his collaborators in the 1960s. Solitonic behavior suggested that

the KdV equation must have conservation laws beyond the obvious conservation

laws of mass, energy, and momentum. A fourth conservation law was discovered

by Gerald Whitham and a

fifth one by Kruskal and Zabusky. Several new conservation laws were discovered

by hand by Robert Miura, who also

showed that many conservation laws existed for a related equation known as the

Modified Korteweg–de Vries (MKdV) equation. With these conservation laws, Miura showed a

connection (called the Miura transformation) between solutions of the KdV and

MKdV equations. This was a clue that enabled Kruskal, with Clifford S. Gardner, John M. Greene, and Miura (GGKM), to discover a general technique for exact

solution of the KdV equation and understanding of its conservation laws. This

was the inverse scattering method,

a surprising and elegant method that demonstrates that the KdV equation admits

an infinite number of Poisson-commuting conserved quantities and is completely

integrable. This discovery gave the modern basis for understanding of the

soliton phenomenon: the solitary wave is recreated in the outgoing state

because this is the only way to satisfy all of the conservation laws. Soon

after GGKM, Peter Lax famously interpreted the inverse scattering method in

terms of isospectral deformations and so-called "Lax pairs". The

inverse scattering method has had an astonishing variety of generalizations and

applications in different areas of mathematics and physics. Kruskal himself

pioneered some of the generalizations, such as the existence of infinitely many