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.
JMAA 145 1990 52-62.pdf
- 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 & Ganghoffer, J-F, On the nonlocal symmetries, group invariant solutions and
conservation laws of the equations of nonlinear dynamical compressible elasticitiy. Proceedings of IUTAM
Symposium on Progress in the Theory and Numerics of Configurational Mechanics, P. Steinmann (ed.), Springer,
(2009), 107-120.
IUTAM2009.pdf
- Bluman, G, Cheviakov, A & Anco, S, Construction of conservation laws: how the direct method generalizes
Noethers theorem, Proceedings of the Fourth International Workshop Group Analysis of Differential Equations
and Integrable Systems, (2010) pp. 13-35.
cyprus proceedings paper.pdf
- Bluman, G., Broadbridge, P., King, J.R, and Ward, M.J., Similarity: generalizations, applications and
open problems, Journal of Engineering Mathematics, 66 (2010), 1-9.
JEngMath6620101-9.pdf
- Cheviakov, A & Bluman, G., On locally and nonlocally related potential systems, J. Math. Phys. 51
(2010) 073502 (23 journal pages)
jmp512010073502.pdf
- Cheviakov, A and Bluman, G, Multidimensional partial differential equations systems: Generating new
systems via conservation laws, potentials, gauges, subsystems. J. Math. Phys. 51 (2010) 103521 (26 journal pages)
jmp512010103521.pdf
- Cheviakov, A and Bluman, G, Multidimensional partial differential equations systems: Nonlocal
symmetries, nonlocal conservation laws, exact solutions. J. Math. Phys. 51 (2010) 103522 (26 journal pages)
jmp512010103522.pdf
- Bluman, G and Ganghoffer, J-F. Connecting Euler and Lagrange systems as nonlocally related system
of dynamical nonlinear elasticity. Arch. Mech. 63 (2011), 363-382.
bluman-ganghoffer3.pdf
- Bluman, G and Dridi, R. New solutions for ordinary differential equations, Journal of Symbolic
Computation 47 (2012), 76-88.
article30JSC dridi.pdf
- Adamuti-Trache, M, Bluman, G, and Tiedje, T. Student Performance in first year university Physics
and Mathematics courses, International Journal of Science Education 35 (2013), 2905-2927.
int journal of science education November 2013.pdf
- Bluman, G, Tian, Shou-fu, Yang, ZZ, Nonclassical analysis of the nonlinear Kompaneets equation,
Journal of Engineering Mathematics, online July 3, 2012, 11pp.
nonlinear kompaneets eqn.pdf
- Bihlo, Alexander and Bluman, G. Conservative parametrization schemes. J. Math. Phys. 54 (2013) 083101, 24 pp.
conservarive parametrization schemes.pdf
- Bluman, G and Yang, ZZ. A symmetry-based method for constructing nonlocally related PDE
systems. J. Math. Phys. 54 (2013) 093504, 22 pp.
symmetry based method to construct nonlocally related systems.pdf
- Temuer Chaolu and Bluman, G, An algorithmic method for showing existence of nontrivial nonclassical
symmetries of partial differential equations without solving determining equations,
J. Math. Anal. Appl. 411 (2014), 281-296.
algorithmic method for existence of nonclassical symmetries.pdf
-
Bluman, G and Yang, ZZ, Some Recent Developments in Finding Systematically Conservation Laws and Nonlocal Symmetries for Partial Differential Equations, in Similarity and Symmetry Methods: Applications in Elasticity and Mechanics of Materials, Lecture Notes in Applied and Computational Mechanics, Vol. 73, J-F Ganghoffer and I Mladenov (eds.), Springer (2014), 1-59.
-
Bluman, George W., Tian, Shou-fu; Yang, Zhengzheng. Nonclassical analysis of the nonlinear Kompaneets equation. J. Engrg. Math. 84 (2014), 87-97.
-
Buhe, Eerdun, Bluman, George W. Symmetry reductions, exact solutions, and conservation laws of the generalized Zakharov equations. J. Math. Phys. 56 (2015), 101501, 14 pp.
-
Hoskins, J. G., Bluman, G. Higher order symmetries and integrating factors for ordinary differential equations. J. Math. Anal. Appl. 435 (2016), 133-161.
-
Buhe, Eerdun, Bluman, G.; Kara, A. H. Conservation laws for some systems of nonlinear PDEs via the symmetry/adjoint symmetry pair method. J. Math. Anal. Appl. 436 (2016), 94-103.
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Bluman, George W., Mrani-Zentar, Omar; Finlay, Deshin Composition of Lie group elements from basis Lie algebra elements. J. Nonlinear Math. Phys. 25 (2018), 528-557.
-
Bluman, George W.; de la Rosa, Rafael; Bruzón, Maria Santos; Gandarias, Maria Luz, A new symmetry-based method for constructing nonlocally related
PDE systems from admitted multi-parameter groups, J. Math. Phys. 61 (2020), 061503
-
Bluman,George W.; Yüzba??b, Zühal Küçükarslan, How symmetries yield
non-invertible mappings of linear partial differential equations, J. Math.
Anal. Appl., 491 (2020), 124354.
-
Chaolu, Temuer; Tong, Lags; Bluman, George W., Some connections between
classical and nonclassical symmetries of a partial differential equation
and their applications, Mathematics (2020) 8040524.
-
Bluman, George W.; de la Rosa, Rafael; Bruzón, Maria Santos; Gandarias, Maria Luz (2021), Differential invariant method for seeking nonlocally related systems and nonlocal symmetries I: General theory and examples, Proceedings of the Royal Society A 477 (2021), doi.org/10.1098/rspa 2020.0908
-
Bluman, George W.; de la Rosa, Rafael; Bruzón, Maria Santos; Gandarias, Maria Luz, Differential invariant method for seeking nonlocally
related systems and nonlocal symmetries II: Connections with the
conservation law method, Proceedings of the Royal Society A 477 (2021),
doi.org/10.1098/rspa 2020.0909
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, 417pp. Springer, New York, Vo. 168, Appl. Math. Sci. 2010; Chinese edition in English 2015.
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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