Geodesic
Solvability of the derivative nonlinear Schr\"odinger equation and the massive Thirring model
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 322-328

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Here we review some results of J. -H. Lee of the $N\times N$ Zakharov–Shabat system with a polynomial spectral parameter. We define a scattering transform following the set-up of Beals–Coifman [2]. In the $2 \times 2$ cases, we modify the Kaup–Newell and Kuznetsov–Mikhailov system to assure the normalization with respect to the spectral parameter. Then we are able to apply the technique of Zakharov–Shabat for the solitons of NLS to our cases. We obtain the long-time behavior of the equations which can be transformed into DNLS and MTM in laboratory coordinates respectively. 
@article{TMF_1994_99_2_a19,
     author = {Jyh-Hao Lee},
     title = {Solvability of the derivative nonlinear {Schr\"odinger} equation and the massive {Thirring} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {322--328},
     publisher = {mathdoc},
     volume = {99},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a19/}
}
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Jyh-Hao Lee. Solvability of the derivative nonlinear Schr\"odinger equation and the massive Thirring model. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 322-328. http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a19/