Quantum nonlinear Schrödinger equation. I. Intertwining operators

Eugène Gutkin

Annales de l'I.H.P. Analyse non linéaire (1986)

  • Volume: 3, Issue: 4, page 285-314
  • ISSN: 0294-1449

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Gutkin, Eugène. "Quantum nonlinear Schrödinger equation. I. Intertwining operators." Annales de l'I.H.P. Analyse non linéaire 3.4 (1986): 285-314. <http://eudml.org/doc/78115>.

@article{Gutkin1986,
author = {Gutkin, Eugène},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {delta Bose gas; Bethe ansatz; commutation relations; second quantization; quantum nonlinear Schrödinger equation; field theory; intertwining operators; Hamiltonian; Fock space},
language = {eng},
number = {4},
pages = {285-314},
publisher = {Gauthier-Villars},
title = {Quantum nonlinear Schrödinger equation. I. Intertwining operators},
url = {http://eudml.org/doc/78115},
volume = {3},
year = {1986},
}

TY - JOUR
AU - Gutkin, Eugène
TI - Quantum nonlinear Schrödinger equation. I. Intertwining operators
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1986
PB - Gauthier-Villars
VL - 3
IS - 4
SP - 285
EP - 314
LA - eng
KW - delta Bose gas; Bethe ansatz; commutation relations; second quantization; quantum nonlinear Schrödinger equation; field theory; intertwining operators; Hamiltonian; Fock space
UR - http://eudml.org/doc/78115
ER -

References

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  2. [2] B. Davies, Second quantization of the nonlinear Schrödinger equation, J. Phys. A., t. 14, 1981, p. 2631-2644. Zbl0498.35032MR629319
  3. [3] E. Gutkin, Integrable systems with delta-potential, Duke Math. J., t. 49, 1982, p. 1-21. Zbl0517.35026MR650365
  4. [4] E. Gutkin, Conservation laws for the nonlinear Schrödinger equation, Ann. Sci. de l'Inst. H. Poincaré, Anal. n. lin., t. 2-1, 1985, p. 67-74. Zbl0585.35080MR781592
  5. [5] E. Gutkin, Propagation of chaos and the Hopf-Cole transformation, Adv. Appl. Math., 1985, n° 4. Zbl0606.35041MR826591
  6. [6] E. Gutkin and M. Kac, Propagation of chaos and the Burgers equation, SIAM J. Appl. Math., t. 43, 1983, p. 971-980. Zbl0554.35104MR709749
  7. [7] E. Gutkin, Quantum nonlinear Schrödinger equation. II. Explicit solution, preprint. Zbl0692.35089MR933972
  8. [8] E. Lieb and W. Lieniger, Exact analysis of an interacting Bose gas. I. The general solution and the ground state, Phys. Rev., t. 130, 1963, p. 1605-1616. Zbl0138.23001MR156630
  9. [9] W. Magnus, F. Oberhettinger and R.P. Soni, Formulas and theorems for the special functions of mathematical physics, Springer1966. Zbl0143.08502MR232968
  10. [10] S. Oxford, The Hamiltonian of the quantized nonlinear Schrödinger equation, Ph. D. Thesis, UCLA, 1979. 
  11. [11] M. Reed and B. Simon, Methods of modern mathematical physics, II and III. Academic press, 1979. MR751959
  12. [12] H.B. Thacker, The quantum inverse method and Green's functions for completely integrable field theories, in Integrable Quantum Field Theories, LN in Physics, t. 151, Springer1981. 
  13. [13] C.N. Yang, Some exact results for the many-body problem in one dimension with repulsive delta-function interaction, Phys. Rev. Lett., t. 19, 1967, p. 1312-1314. Zbl0152.46301MR261870
  14. [14] V.E. Zakharov and A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Phys. JETP, t. 34, 1972, p. 62-69. MR406174
  15. [15] P.P. Kulish and E.K. Sklyanin, Quantum spectral transform method. Recent developments, in Integrable Quantum Field Theories, LN in Physics, t. 151, Springer1981. Zbl0734.35071MR671263
  16. [16] L.D. Faddeev, Quantum completely integrable models in field theory, Soviet Sci. Rev. C, t. 1, 1980, p. 107-156. Zbl0569.35064
  17. [17] V.E. Zakharov and S.V. Manakov, On the complete integrability of a nonlinear Schrödinger equation, Theor. Math. Phys., t. 19, 1975, p. 551-559. Zbl0298.35016

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