Publications
Papers
- Bluman, G, Construction of Solutions to Partial Differential Equations by the Use
of Transformation Groups, Ph.D. Thesis, Caltech (1967)
http://etd.caltech.edu/etd/available/etd-04082005-155822/unrestricted/Bluman_gw_1968.pdf
- Bluman, G & Cole, J, General similarity solution of the heat equation, J. Math. Mech. 18
(1969), 1025-1042.
http://www.math.ubc.ca/~bluman/jmm
article 1969.pdf
- Bluman, G, Similarity solutions of the one-dimensional Fokker-Planck equation, Internat. J.
Nonlinear Mech., 6 (1971), 143-153.
IntJ.Nomnline.Mech71.pdf
- Bluman, G, Applications of the general similarity solution of the heat equation to
boundary value problems, Quarterly Appl. Math. XXXI (1974), 403-415.
- Bluman, G, Use of group methods for relating linear and nonlinear partial differential
equations, Proceedings of International Conference on Symmetry,
Similarity and Group Theoretic Methods in Mechanics, Calgary, 1974,
203-218
- Milinazzo, F & Bluman, G, Numerical similarity solutions to Stefan Problems, ZAMM 55
(1975), 423-429.
- Bluman, G & Kumei, S, On the remarkable nonlinear diffusion equation , J. Math. Phys.
21 (1980), 1019-1023.
JMP1980.pdf
- Bluman, G, On the transformation of diffusion processes into the Wiener process, SIAM J.
Appl. Math., 39 (1980), 238-247.
SIAM1980.pdf
- Kumei, S & Bluman, G, When nonlinear differential equations are equivalent to linear
differential equations, SIAM J. Appl. Math. 42 (1982), 1157-1173.
SIAM1982.pdf
- Bluman, G, Dimensional Analysis, Modelling and Symmetry, Int. J. of Math Ed. in Science and
Technology, 14 (1983), 259-272.
- Bluman, G, On mapping linear partial differential equations to constant coefficient
equations, SIAM J. Appl. Math., 43 (1983), 1259-1273.
SIAM1983.pdf
- Bluman, G & Gregory, RD, On transformations of the biharmonic equation, Mathematika,
32 (1985), 118-130.
- Bluman, G & Kumei, S, On invariance properties of the wave equation, J. Math. Phys. 28
(1987), 307-318.
blumankumeijmp1987.pdf
- Bluman, G & Tuckwell, H, Techniques for obtaining analytical solutions for Rall's
model neuron, J. of Neuroscience Methods 20 (1987), 151-166.
jneuro.pdf
- Bluman, G & Kumei, S, Exact solutions for wave equations of two-layered media with smooth
transition, J. Math Phys. 29 (1988), 86-96.
JMP1988aTwo-layered.pdf
- Bluman, G, Kumei, S & Reid, G, New classes of symmetries for partial differential
equations, J. Math. Phys. 29 (1988), 806-811.
JMP1988aNewclasses.pdf
- Bluman, G & Reid, G, New symmetries for ordinary differential equations, IMA J.
App. Math., 40 (1988), 87-94.
IMA_JAM1998.pdf
- Bluman, G & Kumei S, Use of group analysis in solving overdetermined systems of ordinary
differential equations, J. Math. Anal. Appl. 138 (1989), 95-105.
JMAA1989aOverdetermined.pdf
- Bluman, G & Reid, G, Sequences of related linear PDE's, J. Math. Anal. Appl. 144 (1989),
565-585.
JMAA1989bSequences.pdf
- Bluman, G, Simplifying the form of Lie groups admitted by a given differential equation, J.
Math. Anal. Appl. 145 (1990), 52-62.
- Bluman, G & Kumei, S, Symmetry-based algorithms to relate partial differential equations.
I. Local symmetries, EJAM 1 (1990), 189-216.
- Bluman, G & Kumei, S, Symmetry-based algorithms to relate partial differential equations.
II. Linearization by nonlocal symmetries, EJAM 1 (1990), 217-223.
- Bluman, G, A reduction algorithm for an ordinary differential equations admitting a solvable
Lie group. SIAM J. Appl. Math 50 (1990), 1689-1705.
SIAM1990aReduction.pdf
- Bluman, G, Invariant solutions for ordinary differential equations, SIAM J. Appl. Math. 50
(1990), 1706-1715.
SIAM1990bInvariant.pdf
- Bluman, G, Potential symmetries, Proceedings of the Annual Seminar of CMS on Lie Theory
Differential Equations and Representation Theory, CRM, Montreal (1990),
85-100.
- Bluman, G, Linearization of PDEs, Springer Lecture Notes in Physics, Vol. 382
(1991) 285-288.
- Bluman, G, Use and construction of potential symmetries, Math. Comput. Modelling, 8 (1993),
1-14.
MathComputModel1993.pdf
- Bluman, G, Potential symmetries and linearization, in "Applications of Analytic and
Geometric Methods to Nonlinear Differential Equations", P.A.
Clarkson (ed.) Kluwer, (1993), 363-373.
- Bluman, G, An overview of potential symmetries, in "Exploiting Symmetry in Applied and
Numerical Analysis", E.L. Allgower et al. (eds.), AMS Lectures in
Applied Mathematics, vol. 29, (1993), 97-109.
- Bluman, G, Potential symmetries and equivalent conservation laws, in "Modern Group
Analysis: advanced analytical and computational methods in mathematical
physics," N. H. Ibragimov et al (eds.), Kluwer, (1993), 71-84.
- Bluman, G & Doran-Wu, P, The use of factors to discover potential systems or
linearizations, Acta Applicandae Mathematicae 41 (1995), 21-43.
- Anco, S & Bluman, G, Derivation of conservation laws from nonlocal symmetries of
differential equations, J. Math. Phys. 37 (1996), 2361-2375.
JMP1996.pdf
- Bluman, G & Shtelen, V, New classes of Schrodinger equations equivalent to the free
particle equation through non-local transformations, J. Phys. A 29 (1996), 4473-4480.
jphysA96.pdf
- Bluman, G, Developments in similarity methods related to pioneering work of Julian
Cole, in Mathematics is for Solving Problems, S L. P. Cook, V. Roytburd,
M. Tulin (eds.), SIAM (1996) 105-118.
- Anco, S & Bluman, G, Direct construction of conservation laws from field equations, Phys.
Rev. Lett. 78 (1997), 2869-2873.
PhysRevLett97.pdf
- Anco, S & Bluman, G, Nonlocal symmetries and nonlocal conservation laws of Maxwell's
equations, J. Math. Phys. 38 (1997), 3508-3532.
JMP1997.pdf
- Anco, S & Bluman, G, Integrating factors and first integrals for ordinary differential
equations, EJAM 9 (1998), 245-259.
EJAM1998.pdf
- Bluman, G, Cook, L. Pamela, Flaherty, Joe, Kevorkian, J, Malmuth, Norman, O'Malley, Robert,
Schwendeman, Donald W & Tulin, Marshall, Julian D. Cole (1925-1999)
Notices of the AMS 47 (2000), 466-473.
- Anco, S & Bluman, G, Direct construction method for conservation laws of partial
differential equations.
Part I: Examples of conservation law classifications, EJAM 13, (2002) 545-566.
EJAM2002(1).pdf
- Anco, S & Bluman, G, Direct construction method for conservation laws of partial
differential equations.
Part II: General treatment, EJAM 13 (2002), 567-585.
EJAM2002(2).pdf
- Bluman, G & Shtelen,V, Nonlocal transformations of Kolmogorov equations into the
Backward heat equation, J. Math. Anal. Appl. 291 (2004), 419-437.
blumanshtelenjmaa.pdf
- Bluman, G & Yan, Z, Nonclassical potential solutions of partial differential equations,
EJAM 16 (2005), 239-261.
http://www.math.ubc.ca/~bluman/bluman
yan ejam.pdf
- Bluman, G, Temuerchaolu & Sahadevan, R, Local and nonlocal symmetries for
nonlinear telegraph equations, J. Math. Phys 46 (2005), 023505 (12 journal pages)
BTSJMP2005.pdf
- Bluman, G & Temeuerchaolu, Conservation laws for nonlinear telegraph equations,
J. Math. Anal Appl. 310 (2005), 459-476.
BTjmaa2005.pdf
- Bluman, G & Temuerchaolu, Comparing symmetries and conservation laws of nonlinear
telegraph equations, J. Math. Phys. 46 (2005), 073513 (14 journal pages)
BTjmp2005.pdf
- Bluman, G, Connections between symmetries and conservation laws., SIGMA, 1 (2005), Paper 011,
16 pages.
http://www.emis.de/journals/SIGMA/2005/Paper011/sigma05-011.pdf
- Bluman, G & Cheviakov,A, Framework for potential systems and nonlocal symmetries:
Algorithmic approach, J. Math. Phys. 46(2005), 123506 (19 journal pages)
bcjmp2005.pdf
- Bluman, G, Temuerchaolu & Anco, S, New conservation laws obtained directly from
symmetry action on a known conservation law, J. Math. Anal. Appl. 322 (2006),
233-250. BTAjmaa2006.pdf
- Bluman, G, Cheviakov, A & Ivanova, N, Framework for nonlocally related partial differential
equations systems and nonlocal symmetries: Extension, simplification, and examples,
J. Math. Phys. 47 (2006) 113505 (23 journal pages)
BCIJMP2006.pdf
- Bluman, G & Cheviakov, A, Nonlocally related systems, linearization and nonlocal
symmetries for the nonlinear wave equation. . Math. Anal. Appl. 333 (2007) 93-111.
Bcjmaa2007.pdf
- Bluman, G, Cheviakov, A & Senthilvelan, M, Solution and asymptotic/blow-up
behaviour of a class of nonlinear dissipative systems J. Math. Anal. Appl. 339 (2008) 1199-1209.
BCSjmaa2008.pdf
- Anco, S, Bluman, G & Wolf, T, Invertible mappings of nonlinear PDEs
to linear PDEs through admitted conservation laws, Acta Appl. Math 101 (2008) 21-38.
ACTA2008.pdf
- Bluman, G, Nonlocal extensions of similarity methods, J. Nonlin. Math. Phys. 15 (2008) 1-24.
JNLMP2008.pdf
- Bluman, G, Cheviakov, A & Ganghoffer, J-F, Nonlocally related PDE systems for
one-dimensional nonlinear elastodynamics, J. Eng. Math. 62 (2008) 203-221.
JEngMath2008.pdf
- Bluman, G, Cheviakov, A and Ganghoffer, J-F, On the nonlocal symmetries, group invariant
solutions and conservation laws of nonlinear dynamical compressible elasticity, 14pp.
To appear in IUTAM proceedings, 2009.
IUTAM2009.pdf
- Bluman, G, Cheviakov, A and Anco, S, Construction of conservation laws: how the direct method
generalizes Noether’s theorem, 23pp. To appear in proceedings of conference on
Symmetry and Integrability (Cyprus), 2009.
Books
- Group Properties of Differential Equations (translation with numerous corrections of book in
Russian by LV Ovsiannikov), 1967.
- Bluman, G & Cole, J, Similarity Methods for Differential Equations, Springer-Verlag New
York, Heidelberg, Berlin, 1974, 332 pp (Vol. 13, Appl. Math. Sci.).
- Bluman, G, Problem Book for First Year Calculus, Springer-Verlag, New York, Berlin,
Heidelberg, Tokyo, 1984, 384 pp, clothbound; 1985, paperback.
- Bluman, G & Maskall, D, Problems for Grade 12 Mathematics Students Useful as
Preparation for the Euclid Mathematics Contest and/or First Year
Calculus. Dept. of Math., UBC, 1985, 113 pp (revised,1986).
- Bluman, G & Kumei, S, Symmetries
and Differential Equations, Springer-Verlag New York, Heidelberg, Berlin,
1989, 412 pp (Vol. 81, Appl. Math. Sci; reprinted with corrections, 1996);
Chinese edition, 1991.
- Bluman, G & Anco, S, Symmetry and Integration Methods for Differential Equations,
Springer, New York, 2002, 420 pp (Vol. 154, Appl. Math. Sci; Chinese
edition, 2004; Chinese edition in English (see www.wpcbj.com.cn) 2004; Chinese
translation (see www.sciencep.com)
2009
- Bluman, G, Cheviakov, A & Anco, S, Applications of Symmetry Methods to Partial
Differential Equations, Springer, New York. Expected date of publication: November 2009.
Book Reviews
- "Symposium Transsonicum II (IUTAM)", Canadian Aeronautics and Space Journal,
24 (1978), 57-58.
- "Group Invariance in Engineering Boundary Value Problems", by R. Seshadri and T.Y.
Na, SIAM Review, 28 (1986), 248-249.
- "Application of Lie Groups to Differential Equations", by Peter Olver, Vol. 107 of GTM,
AMS Bulletin 18 (1988), 73-78.
- "Nonlinear Boundary Value Problems in Science and Engineering" by C. Rogers
and W.F. Ames, SIAM Review 33 (1991), 294-296.
- "Differential Equations and Group Methods" by J. M. Hill, SIAM Review 36 (1994), 117.
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