Solutions of Some Wave Mechanics Models

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

We consider one-dimensional second order partial differential equations describing waves in inhomogeneous and nonlinear media. Contact transformations and Euler differential substitution are used to construct general solutions. General and partial solutions of some nonstationary continuum mechanics models are found.

Sobre autores

O. Kaptsov

Institute of Computational Modelling SB RAS

Autor responsável pela correspondência
Email: kaptsov@icm.krasn.ru
Russia, Krasnoyarsk

D. Kaptsov

Institute of Computational Modelling SB RAS

Autor responsável pela correspondência
Email: hot.dok@gmail.com
Russia, Krasnoyarsk

Bibliografia

  1. Brekhovskikh L.M. Waves in Layered Media. Moscow: Nauka, 1973. (in Russian)
  2. Kulikovskii A.G., Sveshnikova Elena I. Nonlinear Waves in Elastic Media. Boca Raton. CRC Press, 1995.
  3. Ovsyannikov L.V. Lectures on Basic Gas Dynamics., Moscow; Izhevsk: Inst. Comput. Sci., 2003. (in Russian)
  4. Rabotnov Yu.N. Elements of Hereditary Mechanics of Solids. Moscow: Nauka, 1977. (in Russian)
  5. Ovsyannikov L.V. Group analysis of differential equations. Moscow: Nauka, 1978. (in Russian)
  6. Ibragimov N. Transformation Groups in Mathematical Physics. Dordrecht: Reidel, 1985.
  7. Zakharov V.E., Manakov S.V., Novikov S.P., Pitaevskii L.P. Soliton Theory: Inverse Scattering Method. Moscow: Nauka, 1980.
  8. Ablowitz M.J., Segur H. Solitons and the Inverse Scattering Transform. Philadelphia: Soc. Industr.&Appl. Math., 1981.
  9. Sidorov A.F., Shapeev V.P., Yanenko N.N. Method of Differential Relations and Its Applications in Gas Dynamics. Novosibirsk: Nauka, 1984.
  10. Euler L. Integral Calculus. Vol. 3. Moscow: GIFML, 1958.
  11. Darboux J.G. Lectures on the General Theory of Surfaces and Geometrical Applications of the Analysis of Infinitesimals. Vol. 2. Izhevsk: Inst. Comput. Sci., 2013.
  12. Kaptsov O.V. Methods for Integrating Partial Differential Equations. Moscow: Fizmatlit, 2009. (in Russian)
  13. Cherny G.G. Gas Dynamics. Moscow: Nauka, 1988. (in Russian)
  14. Novatsky V.K. Wave Problems of the Theory of Plasticity. Moscow, Mir, 1978.
  15. Medwin H., Clay C. Fundamentals of Acoustical Oceanography. Acad. Press, 1997.
  16. Ames W.F., Lohner R.J., Adams E. Group properties of // Int. J. Nonlin. Mech., 1981, vol. 16, pp. 439–447.
  17. Bluman G.W., Kumei S. On invariance properties of the wave equation // J. Math. Phys., 1987, vol. 28, pp. 307–318.
  18. Bluman G.W., Cheviakov A.F. Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation// J. Math. Anal. Appl., 2007, vol. 333, pp. 93–111.
  19. Pelinovsky E., Kaptsov O. Traveling waves in shallow seas of variable depths // Symmetry, 2022, vol. 14 (7), pp. 1448.
  20. Aksenov A.V. Symmetries and relations between solutions of the class Euler–Poisson–Darboux equations // Dokl. Math., 2001, vol. 64, no. 3, pp. 421–424.
  21. Kamke E. Handbook on First Order Partial Differential Equations. Moscow: Nauka, 1966.
  22. Galaktionov V., Svirshchevskii S. Exact Solutions and Invariant Subspaces of Nonlinear PDEs in Mechanics and Physics. Chapman&Hall/CRC Appl. Math.&Nonlin. Sci., 2006.

Declaração de direitos autorais © О.В. Капцов, Д.О. Капцов, 2023

Este site utiliza cookies

Ao continuar usando nosso site, você concorda com o procedimento de cookies que mantêm o site funcionando normalmente.

Informação sobre cookies