Skip to main content
Log in

Cauchy problem for the generalized Kadomtsev-Petviashvili equation

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. B. B. Kadomtsev and V. I. Petviashvili, “On the stability of solitary waves in weakly dispersive systems,” Dokl. Akad. Nauk SSSR,192, No. 4, 753–756 (1970).

    Google Scholar 

  2. M. Ablowitz and H. Segur, Solitons and the Inverse Problem Method [Russian translation], Mir, Moscow (1987).

    Google Scholar 

  3. R. Grimshaw, “Evolution equations for weakly nonlinear long internal waves in a rotating fluid,” Stud. Appl. Math.,73, No. 1, 1–33 (1985).

    Google Scholar 

  4. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  5. M. Ablowitz, D. Bar Yaacov, and A. S. Fokas, “On the inverse scattering transform for the Kadomtsev-Petviashvili equation,” Stud. Appl. Math.,69, No. 2, 135–143 (1983).

    Google Scholar 

  6. S. V. Manakov, “The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation,” Physica D,3, Nos. 1, 2, 420–427 (1981).

    Google Scholar 

  7. A. S. Fokas and M. J. Ablowitz, “On the inverse scattering of the time-dependent Schrödinger equation and the associated Kadomtsev-Petviashvili (I) equation,” Stud. Appl. Math.,69, No. 3, 211–228 (1983).

    Google Scholar 

  8. M. Schwarz, Jr., “Periodic solutions of Kadomtsev-petviashvili,” Adv. Math.,66, No. 3, 217–233 (1987).

    Google Scholar 

  9. I. M. Krichever, “Periodic problem for the Kadomtsev-Petviashvili equation,” Dokl. Akad. Nauk SSSR,298, No. 4, 802–807 (1988).

    Google Scholar 

  10. A. V. Faminskii, “On the Cauchy problem for the Kadomtsev-Petviashvili equation,” Ukr. Mat. Zh.,45, No. 1, 193–194 (1990).

    Google Scholar 

  11. S. N. Kruzhkov and A. V. Faminskii, “Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation,” Mat. Sb.,120, No. 3, 396–425 (1983).

    Google Scholar 

  12. T. Kato, “On the Cauchy problem for the (generalized) Korteweg-de Vries equation,” Stud. Appl. Math. Adv. Math. Suppl. Stud.,8, 93–128 (1983).

    Google Scholar 

  13. A. V. Faminskii, “The Cauchy problem for the Korteweg-de Vries equation and its generalizations,” Tr. Sem. I. G. Petrovskogo,13, 56–105 (1988).

    Google Scholar 

  14. A. V. Faminskii, “The Cauchy problem for quasilinear equations of odd order,” Mat. Sb.,180, No. 9, 1183–1210 (1989).

    Google Scholar 

  15. O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  16. J.-L. Lions, Some Methods of Solving Nonlinear Boundary Value Problems [Russian translation], Mir, Moscow (1972).

    Google Scholar 

Download references

Authors

Additional information

Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 1, pp. 160–172, January–February, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Faminskii, A.V. Cauchy problem for the generalized Kadomtsev-Petviashvili equation. Sib Math J 33, 133–143 (1992). https://doi.org/10.1007/BF00972945

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00972945

Keywords

Navigation