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2000 | 74 | 1 | 261-274
Tytuł artykułu

Some constructive applications of $Λ^{2}$-representations to integration of PDEs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Two new applications of $Λ^{2}$-representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane $Λ^{2}$. 2. Employing $Λ^{2}$-representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.
Rocznik
Tom
74
Numer
1
Strony
261-274
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-07-20
poprawiono
2000-10-26
Twórcy
autor
  • Chair of Mathematics, Department of Physics, Moscow State University, Moscow, 119899, Russia
  • Chair of Mathematics, Department of Physics, Moscow State University, Moscow, 119899, Russia
Bibliografia
  • [1] M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981.
  • [2] E. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, Paris, 1945.
  • [3] A. G. Popov, The non-Euclidean geometry and differential equations, in: Banach Center Publ. 33, Inst. Math., Polish Acad. Sci., 1996, 297-308.
  • [4] E. G. Poznyak and A. G. Popov, Lobachevsky geometry and the equations of mathematical physics, Russian Acad. Sci. Dokl. Math. 48 (1994), 338-342.
  • [5] E. G. Poznyak and A. G. Popov, Non-Euclidean geometry: Gauss formula and PDE's interpretation, Itogi Nauki i Tekhniki (VINITI), Geometry 2 (1994), 5-24 (in Russian).
  • [6] E. G. Poznyak and A. G. Popov, Geometry of the sine-Gordon equation, Itogi Nauki i Tekhniki (VINITI), Problems of Geometry, 23 (1991), 99-130 (in Russian).
  • [7] E. G. Poznyak and A. G. Popov, The Sine-Gordon Equation: Geometry and Physics, Znanie, Moscow, 1991 (in Russian).
  • [8] E. G. Poznyak and E. V. Shikin, Differential Geometry, Moscow Univ. Press, Moscow, 1990 (in Russian).
  • [9] A. A. Samarskĭ, Theory of Difference Schemes, Nauka, Moscow, 1977 (in Russian).
  • [10] R. Sasaki, Soliton equations and pseudospherical surfaces, Nuclear Phys. B 154 (1979), 343-357.
  • [11] A. S. Smogorzhevskiĭ, Geometric Constructions on the Lobachevsky Plane, Gostekhteorizdat, Moscow, 1951 (in Russian).
  • [12] L. A. Takhtadzhyan and L. D. Faddeev, Hamiltonian Approach in Soliton Theory, Nauka, Moscow, 1986 (in Russian).
  • [13] S. A. Zadadaev, $Λ^{2}$-representations of equations of mathematical physics and formulation of the spectral-evolutionary problem, Vestnik Moskov. Univ. Fiz. Astronom. 1998, no. 5, 29-32 (in Russian).
  • [14] V. E. Zakharov and L. D. Faddeev, Korteweg-de Vries equation is a completely integrable Hamiltonian system, Funktsional. Anal. i Prilozhen. 5 (1971), no. 4, 18-127 (in Russian).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv74z1p261bwm
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