Geodesic
The generalized Zakharov–Shabat system and the soliton perturbations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 292-299 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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