Skip to main content
Log in

Differential Identities for Nonlinear Partial Differential Equations

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We obtain new algebraic analytic presentations for solutions and coefficients of nonlinear second order differential equations and systems of such equations. Bibliography: 18 titles.

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.

Similar content being viewed by others

References

  1. Yu. E. Anikonov, N. B. Ayupova, V. G. Bardakov, V. P. Golubyatnikov, and M. V. Neshchadim, “Inversion of mapping and inverse problems” [in Russian], Sib. Elektron. Mat. Izv. 9, 382–432, electronic only (2012).

  2. Yu. E. Anikonov and M. V. Neshchadim, “Representations of solutions, coefficients, and symbols of operator of evolution equations and inverse problems” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 10, No. 2, 25–36 (2010); English transl.: J. Math. Sci., New York 186, No. 3, 352–363 (2012).

  3. Yu. E. Anikonov and M. V. Neshchadim, “On analytical methods in the theory of inverse problems of mathematical physics” [in Russian], Sib. Elektron. Mat. Izv. 7, 11–61, electronic only (2010).

  4. Yu. E. Anikonov and M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. I” [in Russian], Sib. Zh. Ind. Mat. 14, No. 1, 27–39 (2011); English transl.: J. Appl. Ind. Math. 5, No. 4, 506–518 (2011).

  5. Yu. E. Anikonov and M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. II” [in Russian], Sib. Zh. Ind. Mat. 14, No. 2, 28–33 (2011); English transl.: J. Appl. Ind. Math. 6, No. 1, 6–11 (2012).

  6. Yu. E. Anikonov and M. V. Neshchadim, “Analytical methods of the theory of inverse problems for parabolic equations” [in Russian], Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. 11, No. 3, 20–35 (2011); English transl.: J. Math. Sci., New York 195, No. 6, 754– 770 (2013).

  7. Yu. E. Anikonov and M. V. Neshchadim, “On inverse problems for equations of mathematical physics with parameter” [in Russian], Sib. Elektron. Mat. Izv. 9, 45–64, electronic only (2012).

  8. Yu. E. Anikonov and M. V. Neshchadim, “Representations for the solutions and coefficients of second-order differential equations” [in Russian], Sib. Zh. Ind. Mat., 15, No. 4, 17–23 (2012); English transl.: J. Appl. Ind. Math. 7, No. 1, 15–21 (2013).

  9. Yu. E. Anikonov and M. V. Neshchadim, “Representations for the solutions and coefficients of evolution equations” [in Russian], Sib. Zh. Ind. Mat. 16, No. 2, 40–49 (2013); English transl.: J. Appl. Ind. Math. 7, No. 3, 326–334 (2013).

  10. A. V. Bitsadze, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1982).

    MATH  Google Scholar 

  11. N. P. Erugin and M. M. Smirnov, “Functionally invariant solutions of differential equations” [in Russian], Differ. Uravn. 17, No. 5, 853–865 (1981); English transl.: Differ. Equations 17, 563–573 (1981).

  12. A. N. Kolmogorov, I. G. Petrovskij, and N. S. Piskunov, “Studies of the diffusion equation combined with increase in the amount of matter and its applications to a problem in biology” [in Russian], Bul. MGU. Mat. i Mekh. 1, No. 6, 1–26 (1937); English transl. in: Selected works of A. N. Kolmogorov, Vol. I, pp. 242–270, Kluwer, Dordrecht (1991).

  13. R. Courant and D. Hilbert, Methods of Mathematical Physics. II: Partial Differential Equations, John Wiley & Sons, New York etc.(1989).

    Book  MATH  Google Scholar 

  14. S. P. Kurdyumov, G. G. Malinetskii, A. B. Potapov, and A. A. Samarskii, “Structures in nonlinear environment” [in Russian], In: Computers and Nonlinear Facts. Informatics and the Modern Science, pp. 5–43, Nauka, Moscow (1988).

  15. M. M. Lavrent’ev, K. G. Reznitskaya, and V. G. Yakhno, One-Dimensional Inverse Problems of Mathematical Physics [in Russian], Nauka, Novosibirsk, (1982).

    MATH  Google Scholar 

  16. L. Ljung, System Identification: Theory for the User, Prentice-Hall, New Jersey (1987).

    MATH  Google Scholar 

  17. J. D. Murray, Mathematical Biology. Vol. 1: An Introduction, Springer, New York (2002).

    MATH  Google Scholar 

  18. J. D. Murray, Mathematical Biology. Vol. 2: Spatial Models and Biomedical Applications, Springer, New York (2003).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu. E. Anikonov.

Additional information

Translated from Vestnik Novosibirskogo Gosudarstvennogo Universiteta: Seriya Matematika, Mekhanika, Informatika 15, No. 1, 2015, pp. 21-28.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anikonov, Y.E., Neshchadim, M.V. Differential Identities for Nonlinear Partial Differential Equations. J Math Sci 215, 436–443 (2016). https://doi.org/10.1007/s10958-016-2849-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-016-2849-3

Keywords

Navigation