Abstract:
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.
Citation:
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