The generalized Zakharov--Shabat system and the soliton perturbations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 292-299

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The nonlinear evolution equations and their inhomogeneous versions related through the inverse scattering method to the generalized Zakharov–Shabat system $L=i d/dx + q(x) -\lambda J$ are studied. Here we assume that the potential $q(x)=[J,Q(x)]$ takes values in the simple Lie algebra $\mathfrak {g}$ and that $J$ is a nonregular element of the Cartan subalgebra $\mathfrak {h}$. The corresponding systems of equations for the scattering data of $L$ are derived. These can be applied to the study of soliton perturbations of such equations as the matrix nonlinear Schrödinger equation, the matrix $n$–wave equations etc.
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     author = {V. S. Gerdjikov},
     title = {The generalized {Zakharov--Shabat} system and the soliton perturbations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {292--299},
     publisher = {mathdoc},
     volume = {99},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a15/}
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V. S. Gerdjikov. The generalized Zakharov--Shabat system and the soliton perturbations. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 292-299. http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a15/