By Evans G. C.
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A recent numerical study of Davydov's fundamental equations confirms his analytical results. A sharp threshold between linear (dispersive) behavior and nonlinear (soliton) formation is clearly seen and this threshold is related to fundamental physical parameters describing the a-helix protein. In the following section we attempt to describe, as carefully as possible for the general reader, the basis for these numerical computations. To this end each term in Davydov's model is physically described with reference 49 INTRODUCTION TO NONLINEAR WAVES to the basic atomic structure.
The prophetic insights of John Scott Russell were completely forgotten. C. Soliton Research from 1945 to 1974 If scientific research had suffered from the spilling of its young blood in the first world war, this mistake was not to be repeated during the second. Poets, perhaps, could still be driven into the guns but not engineers and scientists; they were drafted for more important tasks. S. science, in particular, was greatly strengthened by the war. Not only did we receive several dozen of the very best European scientists as permanent citizens, researchers and teachers; but the forced development of our technological power (in such diverse areas as electronics, microwaves, communications and control, and the manipulation of elementary particles) left us in a state of high morale.
An excellent recent discussion of mathematical results in the study of "reaction-diffusion systems" (of which the nerve fiber system is a special case) has been provided by Paul Fife [1979]. 32 F. SCOTT Current Solitary Wave Research After a gestation period of almost a century and a half, the solitary wave concept has finally been established. It was a difficult birth, but a new paradigm is now a part of our collective scientific thought. The "thingness" of solitary waves in general (and solitons in particular) is widely accepted as a structural basis for viewing and understanding the dynamic behavior of complex nonlinear systems.
A Bohr-Langmuir Transformatio by Evans G. C.
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