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Nonlinear evolution equations associated with energy-dependent Schrödinger potentials. (English) Zbl 0342.35012


MSC:

35J10 Schrödinger operator, Schrödinger equation
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35K55 Nonlinear parabolic equations
35R30 Inverse problems for PDEs
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[1] Ablowitz, M.J., Kaup, D.J., Newel, A.C., and Segur, H., Stud. Appl. Math. 53, 294 (1974), especially Appendix 3. Their work develops that of many others, e.g. [4] [5].
[2] Jaulent, M. and Jean, C., Comm. Math. Phys. 28, 177 (1972) (radial case x?0); also Ann. Hist. Henri Poincaré, to be published (x?IR, U and Q real, our Q becomes 2Q, 250-1, s inf21 {\(\pm\)} ?R {\(\pm\)}). Jaulent, M., J. Math. Phys., to be published (U real, Q purely imaginary).
[3] Agranovich, Z.S. and Marchenko, V.A., The Inverse Problem of Scattering Theory, Gordon and Breach, New York, 1963. · Zbl 0117.06003
[4] Gardner, C.S., Greene, J.M., Kruskal, M.D., and Miura, R.M., Comm. Pure Appl. Math. 27, 97 (1974). · Zbl 0291.35012
[5] Lax, P.D., Comm. Pure Appl. Math. 21, 467 (1968). · Zbl 0162.41103
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