The Linearity of Nonlinear Soliton Equations and the Three Wave Resonance Interaction
The purpose of a school such as this is to provide a background of information for those interested in a given particular subject. The basic fundamentals of solitons have already been well expanded on by the previous talks, and in general, the most that I could add without excessive duplication is simply additional references [Kaup, 1977; Kaup and Newell, 1978a, b; Kaup et al, 1979], which describe my viewpoint on these basics. However, there is one basic point that still has not been emphasized here, and which I have always considered to be striking and important. That is the fact that although these systems are indeed nonlinear, their behavior so closely mocks or imitates linear systems, that one is frequently ahead if he simply forgets that it is nonlinear, and looks upon the system as being essentially linear. For example, Professor Newell [Kaup and Newell, 1978b] has demonstrated a striking representation of the general solution for q in terms of the squared eigenstates.
KeywordsReflection Coefficient Fundamental Solution Inverse Scattering Scattering Problem Linear Solution
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