Abstract
In Chapter I we analyzed the mapping
from the functions Ψ(x), EquationSource% MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafuiQdKLbai % aacaGGOaGaamiEaiaacMcaaaa!39E2!]></EquationSource><EquationSource Format="TEX"><![CDATA[$$\dot \Psi (x)$$ to the transition coefficients and discrete spectrum of the auxiliary linear problem. We saw that for both rapidly decreasing and finite density boundary conditions this “change of variables” makes the dynamics quite simple because the time evolution of the transition coefficients for the continuous and discrete spectra becomes linear.
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Faddeev, L.D., Takhtajan, L.A. (2007). The Riemann Problem. In: Hamiltonian Methods in the Theory of Solitons. Springer Series in Soviet Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69969-9_3
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