Geodesic
Inverse scattering method with variable spectral parameter
Teoretičeskaâ i matematičeskaâ fizika, Tome 70 (1987) no. 3, pp. 323-341

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In the traditional scheme of the inverse scattering method the spectral parameter of the auxiliary linear problem is usually considered as a constant. The authors propose to consider it as a variable satisfying an over-determined system of differential equations which is determined by the auxiliary linear problem. Nonlinear equations arising in this approach include, as a rule, the explicit dependence on coordinates. Besides the known equations (equation of gravitation, Heisenberg equation in axial geometry etc.) the method makes it possible to construct a number of new integrable equations valuable for applications. 
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     author = {S. P. Burtsev and V. E. Zakharov and A. V. Mikhailov},
     title = {Inverse scattering method with variable spectral parameter},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--341},
     publisher = {mathdoc},
     volume = {70},
     number = {3},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_70_3_a0/}
}
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S. P. Burtsev; V. E. Zakharov; A. V. Mikhailov. Inverse scattering method with variable spectral parameter. Teoretičeskaâ i matematičeskaâ fizika, Tome 70 (1987) no. 3, pp. 323-341. http://geodesic.mathdoc.fr/item/TMF_1987_70_3_a0/