Construction of a transformation operator. (English) Zbl 0842.34087
Summary: We are concerned with the explicit construction of the kernel of the transformation operator used in the scattering theory associated with the Gelfand-Levitan-Marchenko equations. The kernel of the transmutation is well known to play an important role in the inverse scattering theory, and nonlinear integrable systems such as KdV equations. Our method uses operational calculus.
MSC:
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 81U40 | Inverse scattering problems in quantum theory |
| 34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
References:
| [1] | DOI: 10.1090/S0002-9939-1991-1021896-3 · doi:10.1090/S0002-9939-1991-1021896-3 |
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