Skip to main content
Log in

Local and nonlocal currents for nonlinear equations

  • Published:
Theoretical and Mathematical Physics 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. V. S. Vladimirov, The Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  2. G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York (1974).

    Google Scholar 

  3. L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. N. Kh. Ibragimov, Transformation Groups in Mathematical Physics [in Russian], Nauka, Moscow (1983).

    Google Scholar 

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

    Google Scholar 

  6. M. Kruskal, Lect. Notes in Physics,38, 310 (1975).

    Google Scholar 

  7. C. S. Gardner, J. M. Green, M. D. Kruskal, M. M. Miura, Phys. Rev. Lett.,15, 1095 (1967).

    Google Scholar 

  8. N. N. Bogolyubov, “Model Hamiltonian in the theory of superconductivity,” Selected Works, Vol. 3 [in Russian], Naukova Dumka, Kiev (1971), pp. 110–173.

    Google Scholar 

  9. M. Luscher and K. Pohlmeyer, Nucl. Phys. B,137, 46 (1978).

    Google Scholar 

  10. M. Luscher, Nucl. Phys. B,135, 1 (1978).

    Google Scholar 

  11. E. Brezin, C. Itzykson, J. Zinn-Justin, and J.-B. Zuber, Phys. Lett. B,82, 442 (1979).

    Google Scholar 

  12. V. S. Vladimirov and V. V. Zharinov, Diff. Equations,16, 845 (1980).

    Google Scholar 

  13. L. D. Faddeev, “Integrable models in 1+1 dimensional quantum field theory,” Preprint S. Ph. T./82/79, CEN-SACLAY, France (1982).

    Google Scholar 

  14. V. S. Vladimirov and I. V. Volovich, Dokl. Akad. Nauk SSSR,279, 843 (1984);280, No. 2 (1985).

    Google Scholar 

  15. V. S. Vladimirov and I. V. Volovich, Teor. Mat. Fiz.,59, 3 (1984);60, 169 (1984).

    Google Scholar 

  16. N. N. Bogolyubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed., Wiley, New York (1980).

    Google Scholar 

  17. A. Chodos, Phys. Rev. D,20, 915 (1979).

    Google Scholar 

  18. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Academic Press, New York (1975).

    Google Scholar 

  19. M. Lakshmanan, Th. W. Ruijgrok, and C. J. Thompson, Physica (Utrecht),A84, 577 (1976)

    Google Scholar 

  20. S. P. Novikov, Funktsional. Analiz i Ego Prilozhen.,8, 54 (1974).

    Google Scholar 

  21. V. E. Zakharov and A. B. Shabat, Funktsional. Analiz i Ego Prilozhen.,13, 13 (1979).

    Google Scholar 

  22. K. Pohlmeyer, Commun. Math. Phys.,46, 207 (1976).

    Google Scholar 

  23. V. E. Zakharov and A. V. Mikhailov, Zh. Eksp. Teor. Fiz.,74, 1953 (1978).

    Google Scholar 

  24. L. Dolan, “Kac-Moody algebras and exact solvability in hadron physics,” Preprint RU 83/B/63, The Rockefeller University, New York (1983).

    Google Scholar 

  25. L. A. Takhtajan, Phys. Lett. A,64, 235 (1977).

    Google Scholar 

  26. H. Eichenherr, “Infinite dimensional symmetry algebras in integrable systems,” Preprint PAR-LPTHE 82/16, Paris (1982).

  27. W. R. Wasow, Asymptotic Expansions for Ordinary Differential Equations, New York (1965).

  28. V. P. Maslov, Perturbation Theory and Asymptotic Methods [in Russian], MGU, Moscow (1965).

    Google Scholar 

  29. M. Grimm, M. Sohnius, and J. Wess, Nucl. Phys. B,133, 275 (1978).

    Google Scholar 

  30. I. V. Volovich, Teor. Mat. Fiz.57, 469 (1983).

    Google Scholar 

  31. C. Devchand, Nucl. Phys. B,238, 331 (1984).

    Google Scholar 

  32. I. Ya. Aref'eva and I. V. Volovich, Zap. Nauchn. Semin. LOMI,133, 6 (1984).

    Google Scholar 

  33. I. V. Volovich, “Quasiclassical expansion in constructive quantum field theory,” Author's Abstract of Candidate's Dissertation [in Russian], V. A. Steklov Mathematics Institute, USSR Academy of Sciences (1979).

  34. P. P. Kulish, Teor. Mat. Fiz.,26, 198 (1976).

    Google Scholar 

  35. R. K. Dodd and R. K. Bullough, Proc. R. Soc. London Ser. A,352, 481 (1977).

    Google Scholar 

  36. A. V. Zhiber and A. B. Shabat, Dokl. Akad. Nauk SSSR,247, 1103 (1979).

    Google Scholar 

Download references

Authors

Additional information

V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 62, No. 1, pp. 3–29, January, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vladimirov, V.S., Volovich, I.V. Local and nonlocal currents for nonlinear equations. Theor Math Phys 62, 1–20 (1985). https://doi.org/10.1007/BF01034820

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01034820

Keywords

Navigation