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Volumn 39, Issue 2, 1998, Pages 1170-1188

Group analysis and renormgroup symmetries

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[No Author keywords available]

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EID: 0032330122     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532374     Document Type: Article
Times cited : (46)

References (63)
  • 1
    • 0001331745 scopus 로고
    • La normalisation des constantes dans la theorie des quanta
    • in French
    • E. E. C. Stueckelberg and A. Petermann, "La normalisation des constantes dans la theorie des quanta," Helv. Phys. Acta 22, 499-520 (1953) (in French).
    • (1953) Helv. Phys. Acta , vol.22 , pp. 499-520
    • Stueckelberg, E.E.C.1    Petermann, A.2
  • 2
    • 36149023949 scopus 로고
    • Quantum electrodynamics at small distances
    • M. Gell-Mann and F. Low. "Quantum electrodynamics at small distances," Phys. Rev. 95, 1300-1312 (1954).
    • (1954) Phys. Rev. , vol.95 , pp. 1300-1312
    • Gell-Mann, M.1    Low, F.2
  • 3
    • 0001660867 scopus 로고
    • On renormalization group in quantum electrodynamics
    • N. N. Bogoliubov and D. V. Shirkov, "On renormalization group in quantum electrodynamics," Dokl. Akad. Nauk. 103, 203-206 (1955); 103, 391-394 (1955) (in Russian).
    • (1955) Dokl. Akad. Nauk. , vol.103 , pp. 203-206
    • Bogoliubov, N.N.1    Shirkov, D.V.2
  • 4
    • 85033895754 scopus 로고
    • in Russian
    • N. N. Bogoliubov and D. V. Shirkov, "On renormalization group in quantum electrodynamics," Dokl. Akad. Nauk. 103, 203-206 (1955); 103, 391-394 (1955) (in Russian).
    • (1955) Dokl. Akad. Nauk. , vol.103 , pp. 391-394
  • 5
    • 51249193035 scopus 로고
    • Charge renormalization group in quantum field theory
    • N. N. Bogoliubov and D. V. Shirkov, "Charge renormalization group in quantum field theory," Nuovo Cimento 3, 845-863 (1956); see also Sov. Phys. JETP 3, 57 (1956).
    • (1956) Nuovo Cimento , vol.3 , pp. 845-863
    • Bogoliubov, N.N.1    Shirkov, D.V.2
  • 6
    • 51249193035 scopus 로고
    • N. N. Bogoliubov and D. V. Shirkov, "Charge renormalization group in quantum field theory," Nuovo Cimento 3, 845-863 (1956); see also Sov. Phys. JETP 3, 57 (1956).
    • (1956) Sov. Phys. JETP , vol.3 , pp. 57
  • 7
    • 26144461489 scopus 로고
    • Renormalization group and critical phenomena
    • K. Wilson, "Renormalization group and critical phenomena," Phys. Rev. B 4, 3184-3205 (1971).
    • (1971) Phys. Rev. B , vol.4 , pp. 3184-3205
    • Wilson, K.1
  • 9
    • 85033889928 scopus 로고    scopus 로고
    • The generalization to the case of several parameters is straightforward - see, e.g., Refs. 4, 8
    • The generalization to the case of several parameters is straightforward - see, e.g., Refs. 4, 8.
  • 10
    • 0001398076 scopus 로고
    • Renormalization group in modern physics
    • D. V. Shirkov, "Renormalization group in modern physics," Int. J. Mod. Phys. A 3, 1321-1342 (1988).
    • (1988) Int. J. Mod. Phys. A , vol.3 , pp. 1321-1342
    • Shirkov, D.V.1
  • 11
    • 0002270808 scopus 로고
    • Renormalization group, invariance principle and functional self-similarity
    • D. V. Shirkov, "Renormalization group, invariance principle and functional self-similarity," Sov. Phys. Dokl. 27, 197-200 (1982).
    • (1982) Sov. Phys. Dokl. , vol.27 , pp. 197-200
    • Shirkov, D.V.1
  • 12
    • 0345748838 scopus 로고
    • Renormgroup and functional self-similarity in different branches of physics
    • D. V. Shirkov, "Renormgroup and functional self-similarity in different branches of physics," Theor. Math. Phys. 60, 778-782 (1984).
    • (1984) Theor. Math. Phys. , vol.60 , pp. 778-782
    • Shirkov, D.V.1
  • 15
    • 85033900095 scopus 로고    scopus 로고
    • In general this means that S transforms according to some representation of a group
    • In general this means that S transforms according to some representation of a group.
  • 17
    • 85033902664 scopus 로고
    • Strong nonlinearity and generation of high harmonics in laser plasma
    • Kiev, USSR, 6-12 April 1987, edited by A. G. Sitenko Naukova Dumka, Kiev
    • V. F. Kovalev, V. V. Pustovalov, "Strong nonlinearity and generation of high harmonics in laser plasma," in Proceedings of contributed papers of the International Conference on Plasma Physics, Kiev, USSR, 6-12 April 1987, edited by A. G. Sitenko (Naukova Dumka, Kiev, 1987), Vol. 1, pp. 271-273; "Influence of laser plasma temperature on the high harmonics generation process," ibid. pp. 274-277; for details see V. F. Kovalev and V. V. Pustovalov, "Strong nonlinearity and generating of higher harmonics in inhomogeneous plasma," P. N. Lebedev Physical Institute, preprint No. 78, February, 1987 (in Russian).
    • (1987) Proceedings of Contributed Papers of the International Conference on Plasma Physics , vol.1 , pp. 271-273
    • Kovalev, V.F.1    Pustovalov, V.V.2
  • 18
    • 85033888822 scopus 로고    scopus 로고
    • Influence of laser plasma temperature on the high harmonics generation process
    • V. F. Kovalev, V. V. Pustovalov, "Strong nonlinearity and generation of high harmonics in laser plasma," in Proceedings of contributed papers of the International Conference on Plasma Physics, Kiev, USSR, 6-12 April 1987, edited by A. G. Sitenko (Naukova Dumka, Kiev, 1987), Vol. 1, pp. 271-273; "Influence of laser plasma temperature on the high harmonics generation process," ibid. pp. 274-277; for details see V. F. Kovalev and V. V. Pustovalov, "Strong nonlinearity and generating of higher harmonics in inhomogeneous plasma," P. N. Lebedev Physical Institute, preprint No. 78, February, 1987 (in Russian).
    • Proceedings of Contributed Papers of the International Conference on Plasma Physics , pp. 274-277
  • 19
    • 0038885585 scopus 로고
    • P. N. Lebedev Physical Institute, preprint No. 78, February, (in Russian)
    • V. F. Kovalev, V. V. Pustovalov, "Strong nonlinearity and generation of high harmonics in laser plasma," in Proceedings of contributed papers of the International Conference on Plasma Physics, Kiev, USSR, 6-12 April 1987, edited by A. G. Sitenko (Naukova Dumka, Kiev, 1987), Vol. 1, pp. 271-273; "Influence of laser plasma temperature on the high harmonics generation process," ibid. pp. 274-277; for details see V. F. Kovalev and V. V. Pustovalov, "Strong nonlinearity and generating of higher harmonics in inhomogeneous plasma," P. N. Lebedev Physical Institute, preprint No. 78, February, 1987 (in Russian).
    • (1987) Strong Nonlinearity and Generating of Higher Harmonics in Inhomogeneous Plasma
    • Kovalev, V.F.1    Pustovalov, V.V.2
  • 20
    • 0001262057 scopus 로고
    • Functional self-similarity in a problem of plasma theory with electron nonlinearity
    • V. F. Kovalev and V. V. Pustovalov, "Functional self-similarity in a problem of plasma theory with electron nonlinearity," Theor. Math. Phys. 81, 1060-1071 (1990). A detailed discussion of related interesting physical results was presented by these authors in Sov. J. Quantum Electron. 18, 463 (1988); 19, 1454 (1989); Sov. J. Plasma Phys. 15, 27 (1989); 15, 327 (1989).
    • (1990) Theor. Math. Phys. , vol.81 , pp. 1060-1071
    • Kovalev, V.F.1    Pustovalov, V.V.2
  • 21
    • 0001262057 scopus 로고
    • V. F. Kovalev and V. V. Pustovalov, "Functional self-similarity in a problem of plasma theory with electron nonlinearity," Theor. Math. Phys. 81, 1060-1071 (1990). A detailed discussion of related interesting physical results was presented by these authors in Sov. J. Quantum Electron. 18, 463 (1988); 19, 1454 (1989); Sov. J. Plasma Phys. 15, 27 (1989); 15, 327 (1989).
    • (1988) Sov. J. Quantum Electron. , vol.18 , pp. 463
  • 22
    • 0001262057 scopus 로고
    • V. F. Kovalev and V. V. Pustovalov, "Functional self-similarity in a problem of plasma theory with electron nonlinearity," Theor. Math. Phys. 81, 1060-1071 (1990). A detailed discussion of related interesting physical results was presented by these authors in Sov. J. Quantum Electron. 18, 463 (1988); 19, 1454 (1989); Sov. J. Plasma Phys. 15, 27 (1989); 15, 327 (1989).
    • (1989) Sov. J. Quantum Electron. , vol.19 , pp. 1454
  • 23
    • 0001262057 scopus 로고
    • V. F. Kovalev and V. V. Pustovalov, "Functional self-similarity in a problem of plasma theory with electron nonlinearity," Theor. Math. Phys. 81, 1060-1071 (1990). A detailed discussion of related interesting physical results was presented by these authors in Sov. J. Quantum Electron. 18, 463 (1988); 19, 1454 (1989); Sov. J. Plasma Phys. 15, 27 (1989); 15, 327 (1989).
    • (1989) Sov. J. Plasma Phys. , vol.15 , pp. 27
  • 24
    • 0001262057 scopus 로고
    • V. F. Kovalev and V. V. Pustovalov, "Functional self-similarity in a problem of plasma theory with electron nonlinearity," Theor. Math. Phys. 81, 1060-1071 (1990). A detailed discussion of related interesting physical results was presented by these authors in Sov. J. Quantum Electron. 18, 463 (1988); 19, 1454 (1989); Sov. J. Plasma Phys. 15, 27 (1989); 15, 327 (1989).
    • (1989) Sov. J. Plasma Phys. , vol.15 , pp. 327
  • 25
    • 0024795190 scopus 로고
    • Intermediate asymptotics and renormalization group theory
    • N. Goldenfeld, O. Martin, and Y. Oono, "Intermediate asymptotics and renormalization group theory," J. Sci. Comput. 4, 355-372 (1989).
    • (1989) J. Sci. Comput. , vol.4 , pp. 355-372
    • Goldenfeld, N.1    Martin, O.2    Oono, Y.3
  • 26
    • 0000062672 scopus 로고
    • Anomalous dimensions and the renormalization group in a nonlinear diffusion process
    • N. Goldenfield, O. Martin, Y. Oono, and F. Lui, "Anomalous dimensions and the renormalization group in a nonlinear diffusion process," Phys. Rev. Lett. 64, 1361-1364 (1990).
    • (1990) Phys. Rev. Lett. , vol.64 , pp. 1361-1364
    • Goldenfield, N.1    Martin, O.2    Oono, Y.3    Lui, F.4
  • 27
    • 84915503825 scopus 로고
    • Intermediate Asymptotics in math, physics
    • G.I. Barenblatt and Ya.B. Zeldovich, "Intermediate Asymptotics in math, physics," Russ. Math. Surveys 26, 45-61 (1971); "Self-similar solutions as intermediate asymptotics," Annu. Rev. Fluid Mech. 4, 285-312 (1972).
    • (1971) Russ. Math. Surveys , vol.26 , pp. 45-61
    • Barenblatt, G.I.1    Zeldovich, Ya.B.2
  • 28
    • 84915503825 scopus 로고
    • Self-similar solutions as intermediate asymptotics
    • G.I. Barenblatt and Ya.B. Zeldovich, "Intermediate Asymptotics in math, physics," Russ. Math. Surveys 26, 45-61 (1971); "Self-similar solutions as intermediate asymptotics," Annu. Rev. Fluid Mech. 4, 285-312 (1972).
    • (1972) Annu. Rev. Fluid Mech. , vol.4 , pp. 285-312
  • 30
    • 5344281238 scopus 로고    scopus 로고
    • The renormalization group and singular perturbations: Multiple-scales, boundary layers and reductive perturbation theory
    • L.-Y. Chen, N. Goldenfeld, and Y. Oono, "The renormalization group and singular perturbations: Multiple-scales, boundary layers and reductive perturbation theory," Phys. Rev. E 54, 376-394 (1996).
    • (1996) Phys. Rev. E , vol.54 , pp. 376-394
    • Chen, L.-Y.1    Goldenfeld, N.2    Oono, Y.3
  • 31
    • 0000799736 scopus 로고
    • A geometrical formulation of the renormalization group method for global analysis
    • T. Kunihiro, "A geometrical formulation of the renormalization group method for global analysis," Prog. Theor. Phys. 94, 503-514 (1995).
    • (1995) Prog. Theor. Phys. , vol.94 , pp. 503-514
    • Kunihiro, T.1
  • 32
    • 21144479301 scopus 로고
    • RG and the Ginzburg-Landau equation
    • J. Bricmont and A. Kupiainen, "RG and the Ginzburg-Landau equation," Commun. Math. Phys. 150, 193-203 (1992).
    • (1992) Commun. Math. Phys. , vol.150 , pp. 193-203
    • Bricmont, J.1    Kupiainen, A.2
  • 33
    • 84990739185 scopus 로고
    • RG and asymptotics of solutions of nonlinear parabolic equations
    • J. Bricmont, A. Kupiainen, and G. Lin, "RG and asymptotics of solutions of nonlinear parabolic equations," Commun. Pure Appl. Math. 47, 893-922 (1994).
    • (1994) Commun. Pure Appl. Math. , vol.47 , pp. 893-922
    • Bricmont, J.1    Kupiainen, A.2    Lin, G.3
  • 34
    • 0030240068 scopus 로고    scopus 로고
    • Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity
    • J. Bricmont, A. Kupiainen and J. Xin, "Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity," J. Diff. Eqns. 130, 9-35 (1996).
    • (1996) J. Diff. Eqns. , vol.130 , pp. 9-35
    • Bricmont, J.1    Kupiainen, A.2    Xin, J.3
  • 35
    • 0342776648 scopus 로고    scopus 로고
    • Bogolyubov renormgroup
    • D.V. Shirkov, "Bogolyubov renormgroup," Russ. Math. Surveys 49:5, 155-176 (1994) - with numerous misprints; for the corrected version see "The Bogoliubov renormalization group (second English printing)," JINR Commun. E2-96-15; also in hep-th/9602024.
    • (1994) Russ. Math. Surveys , vol.49 , Issue.5 , pp. 155-176
    • Shirkov, D.V.1
  • 36
    • 0342776648 scopus 로고    scopus 로고
    • The Bogoliubov renormalization group
    • also in hep-th/9602024
    • D.V. Shirkov, "Bogolyubov renormgroup," Russ. Math. Surveys 49:5, 155-176 (1994) - with numerous misprints; for the corrected version see "The Bogoliubov renormalization group (second English printing)," JINR Commun. E2-96-15; also in hep-th/9602024.
    • JINR Commun. E2-96-15
  • 38
    • 21844491002 scopus 로고
    • Renormalization group symmetry and sophus Lie group analysis
    • D. V. Shirkov, "Renormalization group symmetry and sophus Lie group analysis," Int. J. Mod. Phys. C 6, 503-512 (1995).
    • (1995) Int. J. Mod. Phys. C , vol.6 , pp. 503-512
    • Shirkov, D.V.1
  • 39
    • 0004171145 scopus 로고    scopus 로고
    • Vol. 1: "Symmetries, exact solutions and conservation laws," Vol. 2: "Applications in engineering and physical sciences," Vol. 3: "New trends in theoretical developments and computational methods."
    • (CRC Press, Boca Raton, FL).
    • CRC Handbook of Lie Group Analysis of Differential Equations, edited by N. H. Ibragimov (CRC Press, Boca Raton, FL). Vol. 1: "Symmetries, exact solutions and conservation laws," Vol. 2: "Applications in engineering and physical sciences," Vol. 3: "New trends in theoretical developments and computational methods."
    • CRC Handbook of Lie Group Analysis of Differential Equations
    • Ibragimov, N.H.1
  • 40
    • 0040833639 scopus 로고
    • On the light scattering by atmospheres of planets
    • (in Russian)
    • To our knowledge the embedding method was originally used by V. A. Ambartzumyan, "On the light scattering by atmospheres of planets," Astronom. J. 19, 30 (1942) (in Russian); later, this method enjoyed wide application to different problems - see, e.g., J. Casti and R. Kalaba, Imbedding Methods in Applied Mathematics (Addison-Wesley, Reading, MA, 1973), and references therein.
    • (1942) Astronom. J. , vol.19 , pp. 30
    • Ambartzumyan, V.A.1
  • 41
    • 0040663593 scopus 로고
    • Addison-Wesley, Reading, MA, and references therein
    • To our knowledge the embedding method was originally used by V. A. Ambartzumyan, "On the light scattering by atmospheres of planets," Astronom. J. 19, 30 (1942) (in Russian); later, this method enjoyed wide application to different problems - see, e.g., J. Casti and R. Kalaba, Imbedding Methods in Applied Mathematics (Addison-Wesley, Reading, MA, 1973), and references therein.
    • (1973) Imbedding Methods in Applied Mathematics
    • Casti, J.1    Kalaba, R.2
  • 45
    • 0038885588 scopus 로고
    • Symmetry group of nonlinear one-dimensional equations of electron plasma
    • V. F. Kovalev, V. V. Pustovalov, "Symmetry group of nonlinear one-dimensional equations of electron plasma," Soviet Physics - Lebedev Institute Reports, No. 2, 1991, pp. 28-31.
    • (1991) Soviet Physics - Lebedev Institute Reports , vol.2 , pp. 28-31
    • Kovalev, V.F.1    Pustovalov, V.V.2
  • 46
    • 0009033318 scopus 로고
    • The renormalization group method based on group analysis
    • edited by D. V. Shirkov and V. B. Priezzev World Scientific, Singapore
    • V. F. Kovalev, S. V. Krivenko, and V. V. Pustovalov, "The renormalization group method based on group analysis," in Renormalization Group-91, edited by D. V. Shirkov and V. B. Priezzev (World Scientific, Singapore, 1992), pp. 300-314.
    • (1992) Renormalization Group-91 , pp. 300-314
    • Kovalev, V.F.1    Krivenko, S.V.2    Pustovalov, V.V.3
  • 47
    • 0038885586 scopus 로고
    • Lie algebra of renormalization group admitted by initial value problem for Burgers equation
    • V. F. Kovalev and V. V. Pustovalov, "Lie algebra of renormalization group admitted by initial value problem for Burgers equation," Lie Groups Appl. 1, 104-120 (1994).
    • (1994) Lie Groups Appl. , vol.1 , pp. 104-120
    • Kovalev, V.F.1    Pustovalov, V.V.2
  • 49
    • 0000909553 scopus 로고
    • Lie-Bäcklund symmetry of nonlinear geometrical optics equations
    • V. F. Kovalev, V. V. Pustovalov, and S. I. Senashov, "Lie-Bäcklund symmetry of nonlinear geometrical optics equations," Differential Equations 29, 1521-1531 (1993).
    • (1993) Differential Equations , vol.29 , pp. 1521-1531
    • Kovalev, V.F.1    Pustovalov, V.V.2    Senashov, S.I.3
  • 50
    • 0040594056 scopus 로고
    • Computer algebra tools in a group analysis of quasi-Chaplygin system of equations
    • edited by B. Denby and D. Perret-Gallix World Scientific, Singapore
    • V. F. Kovalev, "Computer algebra tools in a group analysis of quasi-Chaplygin system of equations," in New Computing Techniques in Physics Research IV, edited by B. Denby and D. Perret-Gallix (World Scientific, Singapore, 1995), p. 229.
    • (1995) New Computing Techniques in Physics Research Iv , vol.4 , pp. 229
    • Kovalev, V.F.1
  • 51
    • 0000816869 scopus 로고    scopus 로고
    • Group and renormgroup symmetry of quasi-Chaplygin media
    • V. F. Kovalev, "Group and renormgroup symmetry of quasi-Chaplygin media," J. Nonlin. Math. Phys. 3, 351-356 (1996).
    • (1996) J. Nonlin. Math. Phys. , vol.3 , pp. 351-356
    • Kovalev, V.F.1
  • 52
    • 0031128095 scopus 로고    scopus 로고
    • Group and renormgroup symmetry of a simple model for nonlinear phenomena in optics, gas dynamics and plasma theory
    • V. F. Kovalev and V. V. Pustovalov, "Group and renormgroup symmetry of a simple model for nonlinear phenomena in optics, gas dynamics and plasma theory," Math. Comput. Mod. 25, 165-179 (1997).
    • (1997) Math. Comput. Mod. , vol.25 , pp. 165-179
    • Kovalev, V.F.1    Pustovalov, V.V.2
  • 53
    • 0000815748 scopus 로고    scopus 로고
    • Renormgroup symmetries in problems of nonlinear geometrical optics
    • in press
    • V. F. Kovalev, "Renormgroup symmetries in problems of nonlinear geometrical optics," Theor. Math. Physics 111 (in press).
    • Theor. Math. Physics , vol.111
    • Kovalev, V.F.1
  • 54
    • 0031328881 scopus 로고    scopus 로고
    • Renormalization group in mathematical physics and some problems of laser optics
    • Dubna, E5-97-41 (in English)
    • V. F. Kovalev and D. V. Shirkov, "Renormalization group in mathematical physics and some problems of laser optics," JINR Preprint, Dubna, 1997, E5-97-41 (in English); J. Nonlin. Opt. Phys. Mat. 6 (in press).
    • (1997) JINR Preprint
    • Kovalev, V.F.1    Shirkov, D.V.2
  • 55
    • 0031328881 scopus 로고    scopus 로고
    • in press
    • V. F. Kovalev and D. V. Shirkov, "Renormalization group in mathematical physics and some problems of laser optics," JINR Preprint, Dubna, 1997, E5-97-41 (in English); J. Nonlin. Opt. Phys. Mat. 6 (in press).
    • J. Nonlin. Opt. Phys. Mat. , vol.6
  • 56
    • 85033902081 scopus 로고    scopus 로고
    • A disadvantage of this is that some examples have a methodological, rather than a physical, significance
    • A disadvantage of this is that some examples have a methodological, rather than a physical, significance.
  • 57
    • 0037823532 scopus 로고
    • GITTL, Moscow-Leningrad, (in Russian)
    • S. A. Chaplygin, On Gas Jets (GITTL, Moscow-Leningrad, 1949) (in Russian).
    • (1949) On Gas Jets
    • Chaplygin, S.A.1
  • 58
    • 0008139499 scopus 로고
    • Unstable quasi-gaseous media
    • B. A. Trubnikov and S. K. Zhdanov, "Unstable quasi-gaseous media," Phys. Rep. 155, 137-230 (1987).
    • (1987) Phys. Rep. , vol.155 , pp. 137-230
    • Trubnikov, B.A.1    Zhdanov, S.K.2
  • 59
  • 60
    • 0001035750 scopus 로고
    • On the self-focusing and self-channeling of intense laser beams in nonlinear medium
    • S. A. Akhmanov, R. V. Khokhlov, and A. P. Sukhorukov, "On the self-focusing and self-channeling of intense laser beams in nonlinear medium," Sov. Phys. JETP 23, 1025-1033 (1966).
    • (1966) Sov. Phys. JETP , vol.23 , pp. 1025-1033
    • Akhmanov, S.A.1    Khokhlov, R.V.2    Sukhorukov, A.P.3
  • 61
    • 0040070051 scopus 로고
    • Group analysis of integro-differential Boltzmann equation
    • Yu. N. Grigoryev and S. V. Meleshko, "Group analysis of integro-differential Boltzmann equation," Sov. Phys. Dokl. 32, 874-876 (1987).
    • (1987) Sov. Phys. Dokl. , vol.32 , pp. 874-876
    • Grigoryev, Yu.N.1    Meleshko, S.V.2
  • 62
  • 63
    • 0000035107 scopus 로고
    • V. F. Kovalev, S. V. Krivenko, and V. V. Pustovalov, "Group analysis of the Vlasov kinetic equations," Differential Equations 29, 1568-1578 (1993); 29, 1712-1721 (1993).
    • (1993) Differential Equations , vol.29 , pp. 1712-1721


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