ピーター・オルバー

出典: フリー百科事典『ウィキペディア(Wikipedia)』

出典: フリー百科事典『ウィキペディア(Wikipedia)』

ピーター・オルバー(Peter Olver、1952年1月11日 - )は微分方程式 (特に偏微分方程式) を専門とするアメリカ合衆国の数学者である。

著書[編集]

  • Olver, P. J. (1986), Applications of Lie Groups to Differential Equations, Springer.
  • Olver, P. J. (1995), Equivalence, Invariants and Symmetry, en:Cambridge University Press.
  • Olver, P. J. (1999), Classical Invariant Theory, en:Cambridge University Press.
  • Olver, P. J.; Shakiban, C. (2006), Applied Linear Algebra, Prentice–Hall.
  • Olver, P. J., & Sattinger, D. H. (Eds.). (2012). Solitons in physics, mathematics, and nonlinear optics. en:Springer Science & Business Media.
  • Olver, P. J. (2014), Introduction to Partial Differential Equations, Springer.
  • Kac, Victor G. (ed.); Olver, Peter J. (ed.); Winternitz, Pavel (ed.); Özer, Teoman (ed.) Symmetries, differential equations and applications. SDEA-III, Istanbul, Turkey, August 14–17, 2017. Selected papers based on the presentations at the conference. Springer Proceedings in Mathematics & Statistics 266. Cham: Springer (ISBN 978-3-030-01375-2). viii, 199 p. (2018).

代表的な論文[編集]

単著[編集]

  • Olver, P. J. (1977). Evolution equations possessing infinitely many symmetries. Journal of Mathematical Physics, 18(6), 1212-1215.
  • Olver, P. J. (1994). Direct reduction and differential constraints. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 444(1922), 509-523.

2000年代[編集]

  • Olver, P. J. (2001). Joint invariant signatures. Foundations of Computational Mathematics, 1(1), 3-68.
  • Olver, P. J. (2001). Geometric foundations of numerical algorithms and symmetry. Applicable Algebra in Engineering, Communication and Computing, 11(5), 417-436.
  • Olver, P. J. (2006). On multivariate interpolation. Studies in Applied Mathematics, 116(2), 201-240.

2010年代[編集]

  • Olver, P. J. (2010). Moving frames and differential invariants in centro-affine geometry. Lobachevskii Journal of Mathematics, 31(2), 77-89.
  • Olver, P. J. (2011). Differential Invariant Algebra. Comtemp. Math, 549, 95-121.

共著[編集]

1980年代[編集]

  • Ball, J. M., Currie, J. C., & Olver, P. J. (1981). Null Lagrangians, weak continuity, and variational problems of arbitrary order. Journal of Functional Analysis, 41(2), 135-174.
  • Benjamin, T. B., & Olver, P. J. (1982). Hamiltonian structure, symmetries and conservation laws for water waves. Journal of Fluid Mechanics, 125, 137-185.
  • Olver, P. J., & Rosenau, P. (1986). The construction of special solutions to partial differential equations. Physics Letters A, 114(3), 107-112.
  • Olver, P. J., & Rosenau, P. (1987). Group-invariant solutions of differential equations. SIAM Journal on Applied Mathematics, 47(2), 263-278.

1990年代[編集]

  • Kichenassamy, S., & Olver, P. J. (1992). Existence and nonexistence of solitary wave solutions to higher-order model evolution equations. SIAM Journal on Mathematical Analysis, 23(5), 1141-1166.
  • Gonzalez-Lopez, A., Kamran, N., & Olver, P. J. (1993). Normalizability of one-dimensional quasi-exactly solvable Schrödinger operators. Communications in mathematical physics, 153(1), 117-146.
  • González‐López, A., Kamran, N., & Olver, P. J. (1992). Lie algebras of vector fields in the real plane. Proceedings of the London Mathematical Society, 3(2), 339-368.
  • Olver, P. J., & Rosenau, P. (1996). Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support. Physical Review E, 53(2).
  • Calabi, E., Olver, P. J., Shakiban, C., Tannenbaum, A., & Haker, S. (1998). Differential and numerically invariant signature curves applied to object recognition. International Journal of Computer Vision, 26(2), 107-135.
  • Olver, P. J., & Sokolov, V. V. (1998). Integrable evolution equations on associative algebras. Communications in Mathematical Physics, 193(2), 245-268.
  • Fels, M., & Olver, P. J. (1998). Moving coframes: I. A practical algorithm. Acta Applicandae Mathematica, 51(2), 161-213.
  • Fels, M., & Olver, P. J. (1999). Moving coframes: II. Regularization and theoretical foundations. Acta Applicandae Mathematica, 55(2), 127-208.

2000年代[編集]

  • Li, Y. A., & Olver, P. J. (2000). Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. Journal of Differential Equations, 162(1), 27-63.
  • Kogan, I. A., & Olver, P. J. (2003). Invariant Euler–Lagrange equations and the invariant variational bicomplex. Acta Applicandae Mathematica, 76(2), 137-193.
  • Olver, P. J., & Pohjanpelto, J. (2005). Maurer–Cartan forms and the structure of Lie pseudo-groups. Selecta Mathematica, 11(1), 99.
  • Olver, P. J., & Pohjanpelto, J. (2008). Moving frames for Lie pseudo–groups. Canadian Journal of Mathematics, 60(6), 1336-1386.

2010年代[編集]

  • Gui, G., Liu, Y., Olver, P. J., & Qu, C. (2013). Wave-breaking and peakons for a modified Camassa–Holm equation. Communications in Mathematical Physics, 319(3), 731-759.
  • Liu, Y., Olver, P. J., Qu, C., & Zhang, S. (2014). On the blow-up of solutions to the integrable modified Camassa–Holm equation. Analysis and Applications, 12(04), 355-368.

関連項目[編集]