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

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Abstract

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

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References

  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].

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  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 ≡R ±). Jaulent, M., J. Math. Phys., to be published (U real, Q purely imaginary).

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  3. Agranovich, Z.S. and Marchenko, V.A., The Inverse Problem of Scattering Theory, Gordon and Breach, New York, 1963.

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  4. Gardner, C.S., Greene, J.M., Kruskal, M.D., and Miura, R.M., Comm. Pure Appl. Math. 27, 97 (1974).

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  5. Lax, P.D., Comm. Pure Appl. Math. 21, 467 (1968).

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Authors and Affiliations

  1. Département de Physique Mathématique, Université des Sciences et Techniques du Languedoc, 34060, Montpellier, Cedex, France

    M. Jaulent & I. Miodek

Authors
  1. M. Jaulent
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  2. I. Miodek
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Additional information

Physique Mathématique et Théorique, Equipe de recherche associée au N.C.R.S. n0 154.

This work has been done as part of the program ‘Recherche Coopérative sur Programme n0 264: Etude interdisciplinaire des problèmes inverses’.

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Jaulent, M., Miodek, I. Nonlinear evolution equations associated with ‘enegry-dependent Schrödinger potentials’. Lett Math Phys 1, 243–250 (1976). https://doi.org/10.1007/BF00417611

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  • DOI: https://doi.org/10.1007/BF00417611

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