ABSTRACT
We will start with a detailed introduction to an operator theoretic approach for the study of soliton equations going back to Marchenko, with a certain focus on projection techniques and reduction. The specific goal will be to construct m × n $ m\times n $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429470462/301849f2-53e7-4646-acba-6259bf733f01/content/inline-math3330.tif"/> -matrix valued solutions for the AKNS system. The applications will mainly concern the mKdV, in comparison with existing results for the NLS. First we discuss solutions that are degenerate in the sense that particle-like waves with coinciding velocity are superposed. Then a complete asymptotic description is given for multiple pole solutions, including wave packets of weakly bound breathers. Finally the collision of vector solitons is studied.
