I'm interested in the soliton stability result given in HERBERT KOCH and DANIEL TATARU's paper "MULTISOLITONS FOR THE CUBIC NLS IN 1-D AND THEIR STABILITY", published in IHES. However, I feel difficulties with the definition of multisolitons, see definition 1.4 in the paper, where the definition uses the Lax pair, Jost solutions and the transmission coefficient. Can anyone give me some references on these concepts?
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A good starting point for Lax pairs and how to find them is:
Mark Hickman, Willy Heremann, Jennifer Larue and Ünal Göktaş "Scaling invariant Lax pairs of nonlinear evolution equations" Applicable Analysis 91(2) (2012) 381-402.
The books cited in references [1], [2] and [4] of that paper provide explanations of Jost solutions and the transmission coefficient.
