ピーター・オルバー

ピーター・オルバー（Peter Olver、1952年1月11日 - ）は、アメリカ合衆国の数学者。専門は、微分方程式（特に偏微分方程式）。

著書
 Olver, P. J. (1986), Applications of Lie Groups to Differential Equations, Springer.
 Olver, P. J. (1995), Equivalence, Invariants and Symmetry, Cambridge University Press.
 Olver, P. J. (1999), Classical Invariant Theory, 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. 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

単著
 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
 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
 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

1980年代
 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
 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
 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
 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
 フランク・オルバー-父

外部リンク
Frank W.J. Olver, mathematician-ワシントン・ポスト (オルバー家の家族構成に関する記載がある)

アメリカ合衆国の数学者
520111
-520111
アメリカ数学会フェロー
偏微分方程式
微分方程式
数学に関する記事
1952年生
存命人物