Nonlinear evolution equations associated with ‘enegry-dependent Schrödinger potentials’

✍ Scribed by M. Jaulent; I. Miodek

• Publisher: Springer
• Year: 1976
• Tongue: English
• Weight: 363 KB
• Volume: 1
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00417611

✦ Synopsis

The 'Inverse Scattering Transform' is used to solve a class of nonlinear equations associated with the inverse problem for the one-dimensional Schr6dinger equation with the energy-dependent potential V(k, x) = U(x) + kQ(x).

1. INTRODUCTION AND SUMMARY OF RESULTS

We present here an extension to 'energy.dependent potentials' of rather recent results obtained by AKNS [1 ]. They used the 'Inverse Scattering Transform' (I.S.T.) to solve certain classes of nonlinear evolution equations. Our extension is based on the solution of the inverse problem for the one-dimensional Schr/Sdinger equation with energy-dependent potential V(k, x) = U(x) + kQ(x) [2] :

Yxx +[ k2-V]y=O, xCR, kEG (l.1