Darboux transformations for SUSY integrable systems: Proceedings of a Workshop Held at Chicago, IL, USA, 12–14 June 1997

  1. Liu, Q. P.
  2. Mañas, Manuel
Book:
Supersymmetry and Integrable Models

Publisher: Springer

ISBN: 978-3-662-14188-5 978-3-662-14187-8

Year of publication: 1998

Pages: 269-281

Type: Book chapter

DOI: 10.1007/BFB0105324 GOOGLE SCHOLAR lock_openOpen access editor

Bibliographic References

  • Athorne C., Nimmo J. J. C. (1990): On the Moutard transformation for integrable partial differential equations. Inv. Prob. 7, 809–826.
  • Bellucci S., Ivanov E., Krivonos S., Pichugin A. (1993): N=2 super Boussinesq hierarchy: Lax pairs and conservation laws. Phys. Lett. B 312, 463–470.
  • Bilal A., Gervais J.-L. (1988): Superconformal algebra and super-KdV equation. Phys. Lett. B 211, 95–100.
  • Chaichain M., Kulish P. P. (1978): On the method of inverse scattering problem and Bäcklund transformations for supersymmetric equations. Phys. Lett. B 78, 413–416.
  • Crum M. M. (1955): Associated Sturm-Liouville systems. Quart. J. Math. 6, 121–127.
  • Darboux G. (1882): Sur une proposition relative aux équations linéaries, C. R. Acad. Sci. Paris 94, 1456–1459.
  • Darboux G. (1896): Leçons sur la théorie générale des surfaces IV. (Gauthier-Villars, Paris). Reprinted in 1972 by (Chelsea Publishing Company, New York).
  • Das A., Sezgin E., Sin S. J. (1992): The super W ∞ symmetry of the Manin-Radul super KP hierarchy. Phys. Lett. B 278, 435–441.
  • Di Vecchia P., Ferrara S. (1977): Classical solutions in two-dimensional supersymmetric field theories. Nucl. Phys. B 130, 93–104.
  • Doliwa A., Santini P. M., Mañas M. (1997): Transformations of Quadrilateral Lattices (preprint).
  • Eisenhart L. P. (1909): A treatise on the differential geometry of curves and surfaces. (Ginn and Co., Boston).
  • Eisenhart L. P. (1923): Transformations of surfaces (Princeton University Press, Princeton). Reprinted in 1962 by (Chelsea Publishing Company, New York).
  • Ferrara S., Girardello L., Sciuto S. (1978): An infinite set of conservation laws of the supersymmetric sine-Gordon theory. Phys. Lett. B 76, 303–306.
  • Guil F., Mañas M. (1996): Darboux transformations for the Davey-Stewartson equations. Phys. Lett. A 217, 1–6.
  • Hammond E. S. (1920): Periodic conjugate nets. Ann. Math. 22, 238–261.
  • Ibort L. A., Martínez Alonso, L., Medina E. (1996): Explicit solutions of supersymmetric KP hierarchies: supersolitons and solitinos. J. Math. Phys. 37, 6157–6172.
  • Inami T., Kanno H. (1991): Lie superalgebraic approach to super Toda lattice and generalized super KdV equations. Commun. Math. Phys. 136, 519–542.
  • Jonas H. (1915): Über die Transformation der konjugierten Systeme and über den gemeinsamen Ursprung der Bianchischen Permutablitätstheoreme. Berl. Math. Ges. Ber. 14, 96.
  • Levi D. (1988): On a new Darboux transformation for the construction of exact solutions of the Schrödinger equation. Inv. Prob. 4, 165–172.
  • Levy L. (1886): Sur quelques équations linéares aux dérivées partieles. J. l'École Polytecnique 56, 6.
  • Liu Q. P. (1995): Darboux transformations for supersymmetric Korteweg-de Vries equations. Lett. Math. Phys. 35, 115–122.
  • Liu Q. P., Mañas M. (1997a): Darboux transformation for the Manin-Radul supersymmetric KdV equation. Phys. Lett. B 394, 337–342.
  • Liu Q. P., Mañas M. (1997b): Crum transformation and Wronskian type solutions for supersymmetric KdV equation, Phys. Lett. B 396, 133–140.
  • Mañas M. (1997): Darboux transformations for the nonlinear Schrödinger equations. J. Phys. A: Math. Gen. 29, 7721–7737.
  • Mañas M., Martínez Alonso L., Medina E. (1994): Additional symmetries, Virasoro constraints and string equations for the super KP hierarchies. Phys. Lett. B 336, 178–182.
  • Manin Yu. I., Radul A. (1985): A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy. Commun. Math. Phys. 98, 65–77.
  • Martínez Alonso L., Medina E. (1995): Tau-function formalism for supersymmetric KP hierarchies. J. Math. Phys. 36, 4898–4913.
  • Mathieu P. (1988a): Superconformal algebra and supersymmetric Korteweg-de Vries equation. Phys. Lett. B 203, 287–291.
  • Mathieu P. (1988b): Supersymmetric extension of the Korteweg-de Vries equation. J. Math. Phys. 29, 2499–2506.
  • Matveev V. B. (1979): Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters. Lett. Math. Phys. 3, 213–216.
  • Matveev V. B., Salle M. A. (1991): Darboux Transformations and Solitons. (Springer-Verlag, Berlin).
  • Morosi C., Pizzocchero L. (1993): On the biHamiltonian structure of the supersymmetric KdV hierarchies: a Lie superalgebraic approach. Commun. Math. Phys. 158, 267–288.
  • Moutard Th. F. (1878): Sur la construction des équations de la forme $$\frac{1}{z}\frac{{\partial ^2 z}}{{\partial x\partial y}}$$ =λ(x, y), qui admettent une intégrale générale explicite. J. l'École Polytecnique 45, 1–11.
  • Mulase M. (1991): A new super KP system and a characterization of the Jacobians of arbitrary algebraic super curves. J. Diff. Geom. 34, 651–680.
  • Nimmo J. J. C. (1993): Darboux transformations in (2+1)-dimensions. In “Applications of analytic and geometric methods to nonlinear differential equations”, ed. Clarkson P. A., (Kluwer Academic Publisher).
  • Oevel W., Popowicz Z. (1991): The biHamiltonian structure of fully supersymmetric Korteweg-de Vries systems. Commun. Math. Phys. 139, 441–460.
  • Rabin J. M. (1991): The geometry of the super KP flows. Commun. Math. Phys. 137, 533–552.
  • Radul A. O. (1988): Algebro-geometric solutions to the super Kadomtsev-Petviashvili hierarchy. In “Seminar on supermanifolds” vol. 28, edited by Leites D. A., report Stockholm University.
  • Roelofs G. H. M., Kersten P. H. M. (1992): Supersymmetric extensions of nonlinear Schrödinger equation: symmetries and coverings. J. Math. Phys. 33, 2185–2206.
  • Stanciu S. (1994): Additional symmetries of supersymmetric KP hierarchies. Commun. Math. Phys. 165, 261–279.
  • Ueno K., Yamada H., Ikeda K. (1989): Algebraic study on the super-KP hierarchy and the ortho-sympletic super-KP hierarchy. Commun. Math. Phys. 124, 57–78.
  • Wadati M., Sanuki H., Konno K. (1975): Relationships among inverse method, Bäcklund transformation and an infinite number of conservation laws. Prog. Theor. Phys. 53, 419–436.
  • Yung C. M. (1993): The N=2 supersymmetric Boussinesq hierarchies. Phys. Lett. B 309, 75–84.