Nonlinear differential–difference equations and Fourier analysis
Mark J. AblowitzClarkson College of Technology, Potsdam, New York 13676J. F. LadikThe Rockefeller University, New York, New York 10021
1976en
ABI
Abstract
The conceptual analogy between Fourier analysis and the exact solution to a class of nonlinear differential–difference equations is discussed in detail. We find that the dispersion relation of the associated linearized equation is prominent in developing a systematic procedure for isolating and solving the equation. As examples, a number of new equations are presented. The method of solution makes use of the techniques of inverse scattering. Soliton solutions and conserved quantities are worked out.
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Cited by 70 references