Martin Kruskal, 81; mathematician's wave research rippled through sciences

Martin Kruskal, the prolific Princeton mathematician whose work provided a theoretical underpinning for a new form of fiber-optic communications, controlled thermonuclear fusion and the study of black holes, died Dec. 26 at his home in Princeton, N.J., after a series of strokes. He was 81.

His death was announced Thursday by Princeton University, where he spent 38 years.

"We have lost a great man, but he left a great legacy for us to celebrate," said Princeton mathematician Ingrid Daubechies. "Martin Kruskal was an outstanding scientist and mathematician who will be remembered for many seminal contributions. He was also an exceptionally generous, friendly and accessible man."

Kruskal was perhaps most famous for his work on the soliton, an unusual form of wave that is able to maintain its integrity when it encounters a second wave.

Two waves running into each other in a body of water, for example, will tend to cancel each other out.

In contrast, a soliton -- which can exist not only in water, but in a variety of other materials -- passes intact through the second wave. That property makes solitons useful for sending multiple signals through fiber-optic cables without interference and will probably be the basis for the next generation of undersea communications cables.

Solitons were first observed in a canal near Edinburgh in 1834 by the young Scottish scientist John Scott Russell. When the canal boat he was studying suddenly stopped, the bow wave formed into a great heap of water and sped down the canal as a single, solitary wave, passing through other waves it encountered. Russell followed it on his horse for more than two miles before finally losing it in the windings of the canal.

The observation languished in the backwaters of science for more than 130 years until the mid-1960s, when Kruskal and Norman J. Zabusky of Bell Laboratories observed a similar wave in the transport of energy in an atomic crystal.

They named the wave a soliton because of its solitary nature and developed the complicated mathematics needed to describe it. Those equations also turned out to describe Russell's wave, and the two were shown to be mathematically equivalent.

In working out the soliton math, Kruskal and his colleagues for the first time developed a general method for solving so-called nonlinear differential equations -- which describe many natural processes but which were previously thought to be unsolvable.