Nonlinear differential–difference equations and Fourier analysis
- 1 June 1976
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 17 (6) , 1011-1018
- https://doi.org/10.1063/1.523009
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.Keywords
This publication has 12 references indexed in Scilit:
- On Some Periodic Toda LatticesProceedings of the National Academy of Sciences, 1975
- Nonlinear differential−difference equationsJournal of Mathematical Physics, 1975
- On the Toda Lattice. II: Inverse-Scattering SolutionProgress of Theoretical Physics, 1974
- Exact N-Soliton Solution of Nonlinear Lumped Self-Dual Network EquationsJournal of the Physics Society Japan, 1973
- A discrete version of the inverse scattering problemJournal of Mathematical Physics, 1973
- Waves in Nonlinear LatticeProgress of Theoretical Physics Supplement, 1970
- Integrals of nonlinear equations of evolution and solitary wavesCommunications on Pure and Applied Mathematics, 1968
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial StatesPhysical Review Letters, 1965
- On SU6-symmetry of elementary particlesPhysics Letters, 1965