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Volumn 28, Issue 6, 1997, Pages 1457-1489

Dynamics and condensation of complex singularities for Burgers' equation I

Author keywords

Asymptotic approximations; Domain of analyticity; Partial differential equations; Pole dynamics

Indexed keywords


EID: 0041810778     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141095289373     Document Type: Article
Times cited : (42)

References (39)
  • 1
    • 0003241821 scopus 로고
    • Solitons and the Inverse Scattering Transform
    • Philadelphia, PA
    • M. J. ABLOWITZ AND H. SEGUR, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, PA, 1981, pp. 203-209.
    • (1981) SIAM , pp. 203-209
    • Ablowitz, M.J.1    Segur, H.2
  • 4
    • 21844507039 scopus 로고
    • Statistics of shocks in Burgers turbulence, II: Tail probabilities for velocities, shock-strengths and rarefaction intervals
    • M. AVELLANEDA, Statistics of shocks in Burgers turbulence, II: Tail probabilities for velocities, shock-strengths and rarefaction intervals, Comm. Math. Phys., 169 (1995), pp. 45-59.
    • (1995) Comm. Math. Phys. , vol.169 , pp. 45-59
    • Avellaneda, M.1
  • 6
    • 0345933730 scopus 로고
    • Complex singularities and the Riemann surface for the Burgers equation
    • Springer-Verlag, Berlin, New York
    • D. BESSIS AND J. D. FOURNIER, Complex singularities and the Riemann surface for the Burgers equation, Research Reports in Physics: Nonlinear Physics, Springer-Verlag, Berlin, New York, 1990, pp. 252-257.
    • (1990) Research Reports in Physics: Nonlinear Physics , pp. 252-257
    • Bessis, D.1    Fournier, J.D.2
  • 7
    • 0345933729 scopus 로고
    • Pole condensation and the Riemann surface associated with a shock in Burgers equation
    • D. BESSIS AND J. D. FOURNIER, Pole condensation and the Riemann surface associated with a shock in Burgers equation, J. Phys. Lett., 45 (1984), pp. L833-L841.
    • (1984) J. Phys. Lett. , vol.45
    • Bessis, D.1    Fournier, J.D.2
  • 10
    • 77956834067 scopus 로고
    • A mathematical model illustrating the theory of turbulence
    • J. M. BURGERS, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech., 1 (1948), pp. 171-199.
    • (1948) Adv. Appl. Mech. , vol.1 , pp. 171-199
    • Burgers, J.M.1
  • 11
    • 84968519480 scopus 로고
    • A simplified version of the abstract Cauchy-Kowalewski theorem with weak singularities
    • R. E. CAFLISCH, A simplified version of the abstract Cauchy-Kowalewski theorem with weak singularities, Bull. Amer. Math. Soc. (N.S.), 23 (1990), pp. 495-500.
    • (1990) Bull. Amer. Math. Soc. (N.S.) , vol.23 , pp. 495-500
    • Caflisch, R.E.1
  • 12
    • 84990617881 scopus 로고
    • Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems
    • R. E. CAFLISCH, N. ERCOLANI, T. Y. HOU, AND Y. LANDIS, Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems, Comm. Pure Appl. Math., 46 (1993), pp. 453-499.
    • (1993) Comm. Pure Appl. Math. , vol.46 , pp. 453-499
    • Caflisch, R.E.1    Ercolani, N.2    Hou, T.Y.3    Landis, Y.4
  • 13
    • 51249187156 scopus 로고
    • Motion of poles and zeros of special solutions of nonlinear and linear partial differential equations and related "solvable" many body problems
    • F. CALOGERO, Motion of poles and zeros of special solutions of nonlinear and linear partial differential equations and related "solvable" many body problems, Nuovo Cimento B (11), 43 (1978), pp. 177-241.
    • (1978) Nuovo Cimento B (11) , vol.43 , pp. 177-241
    • Calogero, F.1
  • 14
    • 0001238977 scopus 로고
    • A fast adaptive multipole algorithm for particle simulations
    • J. CARRIER, L. GREENGARD, AND V. ROKHLIN, A fast adaptive multipole algorithm for particle simulations, SIAM J. Sci. and Stat. Comp., 9 (1988), pp. 669-686.
    • (1988) SIAM J. Sci. and Stat. Comp. , vol.9 , pp. 669-686
    • Carrier, J.1    Greengard, L.2    Rokhlin, V.3
  • 16
    • 51249183312 scopus 로고
    • Pole expansions of nonlinear partial differential equations
    • D. V. CHOODNOVSKY AND G. V. CHOODNOVSKY, Pole expansions of nonlinear partial differential equations, Nuovo Cimento B (11), 40 (1977), pp. 339-353.
    • (1977) Nuovo Cimento B (11) , vol.40 , pp. 339-353
    • Choodnovsky, D.V.1    Choodnovsky, G.V.2
  • 17
    • 0000332692 scopus 로고
    • On a quasi-linear parabolic equation occurring in aerodynamics
    • J. D. COLE, On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math., 9 (1951), pp. 225-236.
    • (1951) Quart. Appl. Math. , vol.9 , pp. 225-236
    • Cole, J.D.1
  • 19
    • 0020891622 scopus 로고
    • L'équation de Burgers deterministe et statistique
    • J. D. FOURNIER AND U. FRISCH, L'équation de Burgers deterministe et statistique, J. Mech. Theory Appl., 2 (1983), pp. 699-750.
    • (1983) J. Mech. Theory Appl. , vol.2 , pp. 699-750
    • Fournier, J.D.1    Frisch, U.2
  • 20
    • 0000751186 scopus 로고
    • Intermittency in nonlinear dynamics and singularities at complex times
    • U. FRISCH AND R. MORF, Intermittency in nonlinear dynamics and singularities at complex times, Phys. Rev. A (3), 23 (1981), pp. 2673-2705.
    • (1981) Phys. Rev. A (3) , vol.23 , pp. 2673-2705
    • Frisch, U.1    Morf, R.2
  • 21
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulations
    • L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comp. Phys., 73 (1987), pp. 325-348.
    • (1987) J. Comp. Phys. , vol.73 , pp. 325-348
    • Greengard, L.1    Rokhlin, V.2
  • 23
    • 0000979532 scopus 로고
    • A method for proving the convergence of the Painlevé expansions of partial differential equations
    • N. JOSHI AND J. A. PETERSEN, A method for proving the convergence of the Painlevé expansions of partial differential equations, Nonlinearity, 7 (1994), pp. 595-602.
    • (1994) Nonlinearity , vol.7 , pp. 595-602
    • Joshi, N.1    Petersen, J.A.2
  • 24
    • 0002327308 scopus 로고
    • Asymptotic expansion of the Pearcey integral near the caustic
    • D. KAMINSKI, Asymptotic expansion of the Pearcey integral near the caustic, SIAM J. Math. Anal., 20 (1989), pp. 987-1005.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 987-1005
    • Kaminski, D.1
  • 25
    • 0347825237 scopus 로고
    • Dynamics of complex singularities for Burgers' equation
    • V. G. Makhankov, ed., World Scientific, Singapore
    • Y. KIMURA, Dynamics of complex singularities for Burgers' equation, in Proc. NEEDS '94, V. G. Makhankov, ed., World Scientific, Singapore, 1995.
    • (1995) Proc. NEEDS '94
    • Kimura, Y.1
  • 26
    • 0002587383 scopus 로고
    • The Korteweg-de Vries Equation and Related Evolution Equations
    • Amer. Math. Soc., Providence, RI
    • M. D. KRUSKAL, The Korteweg-de Vries Equation and Related Evolution Equations, Lectures in Appl. Math., Amer. Math. Soc., Providence, RI, 1974.
    • (1974) Lectures in Appl. Math.
    • Kruskal, M.D.1
  • 27
    • 84972536320 scopus 로고
    • On the abstract Cauchy-Kowalewski theorem
    • L. NIRENBERG, On the abstract Cauchy-Kowalewski theorem, J. Differential Geom., 6 (1972), pp. 561-576.
    • (1972) J. Differential Geom. , vol.6 , pp. 561-576
    • Nirenberg, L.1
  • 28
    • 0002341808 scopus 로고
    • The asymptotic behavior of Pearcey's integral for complex variables
    • R. B. PARIS, The asymptotic behavior of Pearcey's integral for complex variables, Proc. Roy. Soc. London Ser. A, 432 (1991), pp. 391-426.
    • (1991) Proc. Roy. Soc. London Ser. A , vol.432 , pp. 391-426
    • Paris, R.B.1
  • 29
    • 0002969674 scopus 로고
    • Trigonometrische integrale mit nur reellen nullstellen
    • G. PÓLYA, Über trigonometrische integrale mit nur reellen nullstellen, J. Reine Angewandte Math., 158 (1927), pp. 6-18.
    • (1927) J. Reine Angewandte Math. , vol.158 , pp. 6-18
    • Pólya, G.1    Über2
  • 30
    • 6644224525 scopus 로고
    • The inviscid Burgers equation with initial data of Brownian type
    • Z.-S. SHE, E. AURELL, AND U. FRISCH, The inviscid Burgers equation with initial data of Brownian type, Comm. Math. Phys., 148 (1992), pp. 623-641.
    • (1992) Comm. Math. Phys. , vol.148 , pp. 623-641
    • She, Z.-S.1    Aurell, E.2    Frisch, U.3
  • 31
    • 0030543669 scopus 로고    scopus 로고
    • Asymptotic and numerical approximations of the zeros of Fourier integrals
    • D. SENOUF, Asymptotic and numerical approximations of the zeros of Fourier integrals, SIAM J. Math. Anal., 27 (1996), pp. 1102-1128.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1102-1128
    • Senouf, D.1
  • 32
    • 0031484187 scopus 로고    scopus 로고
    • Dynamics and condensation of complex singularities for Burgers' equation II
    • D. SENOUF, Dynamics and condensation of complex singularities for Burgers' equation II, SIAM J. Math. Anal., 28 (1997), pp. 1490-1513.
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 1490-1513
    • Senouf, D.1
  • 33
    • 0347825238 scopus 로고    scopus 로고
    • Pole dynamics and oscillations for complex Burgers equation in the small dispersion limit
    • D. SENOUF, R. CAFLISCH, AND N. ERCOLANI, Pole dynamics and oscillations for complex Burgers equation in the small dispersion limit, Nonlinearity, 9 (1996), pp. 1671-1702.
    • (1996) Nonlinearity , vol.9 , pp. 1671-1702
    • Senouf, D.1    Caflisch, R.2    Ercolani, N.3
  • 34
    • 34249839748 scopus 로고
    • Statistics of shocks in solutions of inviscid Burgers equation
    • Y. G. SINAI, Statistics of shocks in solutions of inviscid Burgers equation, Comm. Math. Phys., 148 (1992), pp. 601-621.
    • (1992) Comm. Math. Phys. , vol.148 , pp. 601-621
    • Sinai, Y.G.1
  • 35
    • 0001140293 scopus 로고
    • Tracing complex singularities with spectral methods
    • C. SULEM, P. L. SULEM, AND H. FRISCH, Tracing complex singularities with spectral methods, J. Comp. Phys., 50 (1983), pp. 138-161.
    • (1983) J. Comp. Phys. , vol.50 , pp. 138-161
    • Sulem, C.1    Sulem, P.L.2    Frisch, H.3
  • 36
    • 0022130031 scopus 로고
    • Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts
    • O. THUAL, U. FRISCH, AND M. HÉNON, Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts, J. Phys., 46 (1985), pp. 1485-1494.
    • (1985) J. Phys. , vol.46 , pp. 1485-1494
    • Thual, O.1    Frisch, U.2    Hénon, M.3
  • 37
    • 84971708910 scopus 로고
    • Integrals with a large parameter. Several nearly coincident saddle points
    • F. URSELL, Integrals with a large parameter. Several nearly coincident saddle points, Proc. Cambridge Philos. Soc., 72 (1972), pp. 49-65.
    • (1972) Proc. Cambridge Philos. Soc. , vol.72 , pp. 49-65
    • Ursell, F.1


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