메뉴 건너뛰기




Volumn 65, Issue 1, 2005, Pages 230-251

Instabilities of wavy patterns governed by coupled burgers equations

Author keywords

Burgers equation; Combustion; Instability; Waves

Indexed keywords

BURGERS EQUATION; GINZBURG-LANDAU (CGL) EQUATION; KURAMOTO-SIVASHINSKY EQUATIONS; MODULATIONAL INSTABILITIES;

EID: 16244401955     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139903432913     Document Type: Article
Times cited : (1)

References (49)
  • 1
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M. C. CROSS AND P. C. HOHENBERG, Pattern formation outside of equilibrium, Rev. Modern Phys., 65 (1993), pp. 851-1112.
    • (1993) Rev. Modern Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 2
    • 84959644006 scopus 로고
    • Non-linear instability theory for a wave system in plane Poiseuille flow
    • K. STEWARTSON AND J. T. STUART, Non-linear instability theory for a wave system in plane Poiseuille flow, J. Fluid Mech., 48 (1971), pp. 529-545.
    • (1971) J. Fluid Mech. , vol.48 , pp. 529-545
    • Stewartson, K.1    Stuart, J.T.2
  • 4
    • 16244381215 scopus 로고
    • Modulated wave motions arising due to the instability of spatially periodic secondary motions
    • in Russian
    • A. A. NEPOMNYASHCHY, Modulated wave motions arising due to the instability of spatially periodic secondary motions, Proc. Perm State Univ., 316 (1974), pp. 105-113 (in Russian).
    • (1974) Proc. Perm State Univ. , vol.316 , pp. 105-113
    • Nepomnyashchy, A.A.1
  • 5
    • 0036013603 scopus 로고    scopus 로고
    • The world of the complex Ginzburg-Landau equation
    • I. S. ARANSON AND L. KRAMER, The world of the complex Ginzburg-Landau equation, Rev. Modern Phys., 74 (2002), pp. 99-143.
    • (2002) Rev. Modern Phys. , vol.74 , pp. 99-143
    • Aranson, I.S.1    Kramer, L.2
  • 6
    • 0002270864 scopus 로고
    • Order-parameter equations for long-wavelength instabilities
    • A. A. NEPOMNYASHCHY, Order-parameter equations for long-wavelength instabilities, Phys. D, 86 (1995), pp. 90-95.
    • (1995) Phys. D , vol.86 , pp. 90-95
    • Nepomnyashchy, A.A.1
  • 7
    • 0000507179 scopus 로고
    • Persistent propagation of concentration waves in dissipative media far from thermal equilibrium
    • Y. KURAMOTO AND T. TSUZUKI, Persistent propagation of concentration waves in dissipative media far from thermal equilibrium, Progr. Theoret. Phys., 55 (1976), pp. 356-369.
    • (1976) Progr. Theoret. Phys. , vol.55 , pp. 356-369
    • Kuramoto, Y.1    Tsuzuki, T.2
  • 8
    • 0000160238 scopus 로고
    • Stability of wavy regimes in a film flowing down an inclined plane
    • A. A. NEPOMNYASHCHY, Stability of wavy regimes in a film flowing down an inclined plane, Fluid Dynam., 9 (1974), pp. 354-359.
    • (1974) Fluid Dynam. , vol.9 , pp. 354-359
    • Nepomnyashchy, A.A.1
  • 9
    • 0013023244 scopus 로고
    • Model equations for wavy viscous film flow
    • AMS, Providence, RI
    • G. M. HOMSY, Model equations for wavy viscous film flow, in Nonlinear Wave Motion, Lectures in Appl. Math. 15, AMS, Providence, RI, 1974, pp. 191-194.
    • (1974) Nonlinear Wave Motion, Lectures in Appl. Math. , vol.15 , pp. 191-194
    • Homsy, G.M.1
  • 10
    • 0000244322 scopus 로고
    • Reduced model showing chemical turbulence
    • T. YAMADA AND Y. KURAMOTO, Reduced model showing chemical turbulence, Progr. Theoret. Phys., 56 (1976), pp. 681-683.
    • (1976) Progr. Theoret. Phys. , vol.56 , pp. 681-683
    • Yamada, T.1    Kuramoto, Y.2
  • 11
    • 0017554878 scopus 로고
    • Non-linear analysis of hydrodynamic instability in laminar flames. 1. Derivation of basic equations
    • G. I. SIVASHINSKY, Non-linear analysis of hydrodynamic instability in laminar flames. 1. Derivation of basic equations, Acta Astronaut., 4 (1977), pp. 1177-1206.
    • (1977) Acta Astronaut. , vol.4 , pp. 1177-1206
    • Sivashinsky, G.I.1
  • 12
    • 0342547655 scopus 로고
    • Wavy motions in a layer of viscous fluid flowing down the inclined plane
    • in Russian
    • A. A. NEPOMNYASHCHY, Wavy motions in a layer of viscous fluid flowing down the inclined plane, Proc. Perm State Univ., 362 (1976), pp. 114-124 (in Russian).
    • (1976) Proc. Perm State Univ. , vol.362 , pp. 114-124
    • Nepomnyashchy, A.A.1
  • 13
    • 0000002511 scopus 로고
    • Dissipative Korteweg-deVries description of Marangoni-benard oscillatory convection
    • A. N. GARAZO AND M. G. VELARDE, Dissipative Korteweg-deVries description of Marangoni-Benard oscillatory convection, Phys. Fluids A, 3 (1991), pp. 2295-2300.
    • (1991) Phys. Fluids A , vol.3 , pp. 2295-2300
    • Garazo, A.N.1    Velarde, M.G.2
  • 15
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • A. C. NEWELL AND J. A. WHITEHEAD, Finite bandwidth, finite amplitude convection, J. Fluid Mech., 38 (1969), pp. 279-303.
    • (1969) J. Fluid Mech. , vol.38 , pp. 279-303
    • Newell, A.C.1    Whitehead, J.A.2
  • 16
    • 0017269252 scopus 로고
    • Nonlinear saturation of dissipative trapped-ion mode by mode-coupling
    • B. I. COHEN, J. A. KROMMES, W. M. TANG, AND M. N. ROSENBLUTH, Nonlinear saturation of dissipative trapped-ion mode by mode-coupling, Nuclear Fusion, 16 (1976), pp. 971-992.
    • (1976) Nuclear Fusion , vol.16 , pp. 971-992
    • Cohen, B.I.1    Krommes, J.A.2    Tang, W.M.3    Rosenbluth, M.N.4
  • 17
    • 0022755962 scopus 로고
    • Viscoelastic behavior of cellular solutions to the Kuramoto-Sivashinsky model
    • U. FRISCH, Z.-S. SHE, AND O. THUAL, Viscoelastic behavior of cellular solutions to the Kuramoto-Sivashinsky model, J. Fluid Mech., 168 (1986), pp. 221-240.
    • (1986) J. Fluid Mech. , vol.168 , pp. 221-240
    • Frisch, U.1    She, Z.-S.2    Thual, O.3
  • 18
    • 0000035179 scopus 로고
    • Laminarizing effects of dispersion in an active-dissipative nonlinear medium
    • H.-C. CHANG, E. A. DEMEKHIN, AND D. I. KOPELEVICH, Laminarizing effects of dispersion in an active-dissipative nonlinear medium, Phys. D, 63 (1993), pp. 299-320.
    • (1993) Phys. D , vol.63 , pp. 299-320
    • Chang, H.-C.1    Demekhin, E.A.2    Kopelevich, D.I.3
  • 19
    • 0001140910 scopus 로고
    • Stability of periodic-waves governed by the modified Kawahara equation
    • D. E. BAR AND A. A. NEPOMNYASHCHY, Stability of periodic-waves governed by the modified Kawahara equation, Phys. D, 86 (1995), pp. 586-602.
    • (1995) Phys. D , vol.86 , pp. 586-602
    • Bar, D.E.1    Nepomnyashchy, A.A.2
  • 20
    • 84956242506 scopus 로고
    • Nonlinear modulational instability of periodic-waves governed by the Kuramoto-Sivashinsky equation
    • A. A. NEPOMNYASHCHY, Nonlinear modulational instability of periodic-waves governed by the Kuramoto-Sivashinsky equation, Europhys. Lett., 31 (1995) pp. 437-441.
    • (1995) Europhys. Lett. , vol.31 , pp. 437-441
    • Nepomnyashchy, A.A.1
  • 21
    • 0345909363 scopus 로고    scopus 로고
    • Short-wavelength instability and transition to chaos in distributed systems with additional symmetry
    • M. I. TRIBELSKII, Short-wavelength instability and transition to chaos in distributed systems with additional symmetry, Uspekhi Fiz. Nauk, 167 (1997), pp. 167-190.
    • (1997) Uspekhi Fiz. Nauk , vol.167 , pp. 167-190
    • Tribelskii, M.I.1
  • 22
    • 0034215317 scopus 로고    scopus 로고
    • Pattern formation with a conservation law
    • P. C. MATTHEWS AND S. M. COX, Pattern formation with a conservation law, Nonlinearity, 13 (2000), pp. 1293-1320.
    • (2000) Nonlinearity , vol.13 , pp. 1293-1320
    • Matthews, P.C.1    Cox, S.M.2
  • 23
    • 0000573274 scopus 로고    scopus 로고
    • Coupled KS-CGL and coupled Burgers-CGL equations for flames governed by a sequential reaction
    • A. A. GOLOVIN, B. J. MATKOWSKY, A. BAYLISS, AND A. A. NEPOMNYASHCHY, Coupled KS-CGL and coupled Burgers-CGL equations for flames governed by a sequential reaction, Phys. D, 129 (1999), pp. 253-298.
    • (1999) Phys. D , vol.129 , pp. 253-298
    • Golovin, A.A.1    Matkowsky, B.J.2    Bayliss, A.3    Nepomnyashchy, A.A.4
  • 24
    • 0035576861 scopus 로고    scopus 로고
    • Traveling and spiral waves for sequential flames with translation symmetry: Coupled CGL-Burgers equations
    • A. A. GOLOVIN, A. A. NEPOMNYASHCHY, AND B. J. MATKOWSKY, Traveling and spiral waves for sequential flames with translation symmetry: Coupled CGL-Burgers equations, Phys. D, 160 (2001), pp. 1-28.
    • (2001) Phys. D , vol.160 , pp. 1-28
    • Golovin, A.A.1    Nepomnyashchy, A.A.2    Matkowsky, B.J.3
  • 25
    • 0001093342 scopus 로고
    • Patterns produced by a short-wave instability in the presence of a zero mode
    • B. A. MALOMED, Patterns produced by a short-wave instability in the presence of a zero mode, Phys. Rev. A, 45 (1992), pp. 1009-1017.
    • (1992) Phys. Rev. A , vol.45 , pp. 1009-1017
    • Malomed, B.A.1
  • 26
    • 0037989866 scopus 로고
    • Spatiotemporal intermittency in a 1D connective pattern - Theoretical-model and experiments
    • F. DAVIAUD, J. LEGA, P. BERGE, P. COULLET, AND M. DUBOIS, Spatiotemporal intermittency in a 1D connective pattern - theoretical-model and experiments, Phys. D, 55 (1992), pp. 287-308.
    • (1992) Phys. D , vol.55 , pp. 287-308
    • Daviaud, F.1    Lega, J.2    Berge, P.3    Coullet, P.4    Dubois, M.5
  • 27
    • 0002099155 scopus 로고
    • Coupled Burgers equations - A model of polydispersive sedimentation
    • S. E. ESIPOV, Coupled Burgers equations - A model of polydispersive sedimentation, Phys. Rev. E, 52 (1995), pp. 3711-3718.
    • (1995) Phys. Rev. E , vol.52 , pp. 3711-3718
    • Esipov, S.E.1
  • 28
    • 0031120026 scopus 로고    scopus 로고
    • Wave-wave interactions in two-fluid cosmic-ray hydrodynamics
    • G. M. WEBB, M. BRIO, G. P. ZANK, AND T. STORY, Wave-wave interactions in two-fluid cosmic-ray hydrodynamics, J. Plasma Phys., 57 (1997), pp. 631-676.
    • (1997) J. Plasma Phys. , vol.57 , pp. 631-676
    • Webb, G.M.1    Brio, M.2    Zank, G.P.3    Story, T.4
  • 29
    • 0041858039 scopus 로고    scopus 로고
    • Limit set of trajectories of the coupled viscous Burgers' equations
    • J. P. NEE AND J. DUAN, Limit set of trajectories of the coupled viscous Burgers' equations, Appl. Math. Lett., 11 (1998), pp. 57-61.
    • (1998) Appl. Math. Lett. , vol.11 , pp. 57-61
    • Nee, J.P.1    Duan, J.2
  • 30
    • 0034679391 scopus 로고    scopus 로고
    • On integrable coupled Burgers-type equations
    • M. V. FOURSOV, On integrable coupled Burgers-type equations, Phys. Lett. A, 272 (2000), pp. 57-64.
    • (2000) Phys. Lett. A , vol.272 , pp. 57-64
    • Foursov, M.V.1
  • 31
    • 0012777640 scopus 로고    scopus 로고
    • Burgers' turbulence with self-consistently evolved pressure
    • J. FLEISCHER AND P. H. DIAMOND, Burgers' turbulence with self-consistently evolved pressure, Phys. Rev. E, 61 (2000), pp. 3912-3925.
    • (2000) Phys. Rev. E , vol.61 , pp. 3912-3925
    • Fleischer, J.1    Diamond, P.H.2
  • 32
    • 0037471521 scopus 로고    scopus 로고
    • On disintegration of near-limit cellular flames
    • M. L. FRANKEL, P. V. GORDON, AND G. I. SIVASHINSKY, On disintegration of near-limit cellular flames, Phys. Lett. A, 310 (2003), pp. 389-392.
    • (2003) Phys. Lett. A , vol.310 , pp. 389-392
    • Frankel, M.L.1    Gordon, P.V.2    Sivashinsky, G.I.3
  • 33
    • 33947127268 scopus 로고
    • Nonlinear waves in nonequilibrium systems of the oscillatory type, Part I
    • B. A. MALOMED, Nonlinear waves in nonequilibrium systems of the oscillatory type, Part I, Z. Phys. B, 55 (1984), pp. 241-248.
    • (1984) Z. Phys. B , vol.55 , pp. 241-248
    • Malomed, B.A.1
  • 34
    • 33947124315 scopus 로고
    • Nonlinear waves in nonequilibrium systems of the oscillatory type, Part II
    • B. A. MALOMED, Nonlinear waves in nonequilibrium systems of the oscillatory type, Part II, Z. Phys. B, 55 (1984), pp. 249-256.
    • (1984) Z. Phys. B , vol.55 , pp. 249-256
    • Malomed, B.A.1
  • 36
    • 0029132357 scopus 로고
    • Kinetic alpha effect in viscosity stratified creeping flows
    • I. KLIAKHANDLER AND G. SIVASHINSKY, Kinetic alpha effect in viscosity stratified creeping flows, Phys. Fluids, 7 (1995), pp. 1866-1871.
    • (1995) Phys. Fluids , vol.7 , pp. 1866-1871
    • Kliakhandler, I.1    Sivashinsky, G.2
  • 37
    • 0023438205 scopus 로고
    • Large-scale flow driven by the anisotropic kinetic alpha-effect
    • U. FRISCH, Z.-S. SHE, AND P. L. SULEM, Large-scale flow driven by the anisotropic kinetic alpha-effect, Phys. D, 28 (1987), pp. 382-392.
    • (1987) Phys. D , vol.28 , pp. 382-392
    • Frisch, U.1    She, Z.-S.2    Sulem, P.L.3
  • 41
    • 0000170396 scopus 로고
    • A 3-dimensional description of solitary waves and their interaction in Marangoni-Benard layers
    • A. A. NEPOMNYASHCHY AND M. G. VELARDE, A 3-dimensional description of solitary waves and their interaction in Marangoni-Benard layers, Phys. Fluids, 6 (1994), pp. 187-198.
    • (1994) Phys. Fluids , vol.6 , pp. 187-198
    • Nepomnyashchy, A.A.1    Velarde, M.G.2
  • 42
    • 0000472620 scopus 로고    scopus 로고
    • Wavy film flows down an inclined plane: Perturbation theory and general evolution equation for the film thickness
    • A. L. FRENKEL AND K. INDIRESHKUMAR, Wavy film flows down an inclined plane: Perturbation theory and general evolution equation for the film thickness, Phys. Rev. E, 60 (1999), pp. 4143-4157.
    • (1999) Phys. Rev. E , vol.60 , pp. 4143-4157
    • Frenkel, A.L.1    Indireshkumar, K.2
  • 43
    • 0041195846 scopus 로고    scopus 로고
    • Effect of anisotropy on morphological instability in the freezing of a hypercooled melt
    • A. A. GOLOVIN AND S. H. DAVIS, Effect of anisotropy on morphological instability in the freezing of a hypercooled melt, Phys. D, 116 (1998), pp. 363-391.
    • (1998) Phys. D , vol.116 , pp. 363-391
    • Golovin, A.A.1    Davis, S.H.2
  • 44
    • 0040357278 scopus 로고    scopus 로고
    • Stability of periodic waves generated by long-wavelength instabilities in isotropic and anisotropic systems
    • D. E. BAR AND A. A. NEPOMNYASHCHY, Stability of periodic waves generated by long-wavelength instabilities in isotropic and anisotropic systems, Phys. D, 132 (1999), pp. 411-427.
    • (1999) Phys. D , vol.132 , pp. 411-427
    • Bar, D.E.1    Nepomnyashchy, A.A.2
  • 45
    • 0004195621 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • S. H. DAVIS, Theory of Solidification, Cambridge University Press, Cambridge, UK, 2001.
    • (2001) Theory of Solidification
    • Davis, S.H.1
  • 46
    • 0029292815 scopus 로고
    • Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems
    • A. J. BERNOFF, R. KUSKE, B. J. MATKOWSKY, AND V. A. VOLPERT, Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems, SIAM J. Appl. Math., 55 (1995), pp. 485-519.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 485-519
    • Bernoff, A.J.1    Kuske, R.2    Matkowsky, B.J.3    Volpert, V.A.4
  • 47
    • 0001434008 scopus 로고
    • Self organized spiral and circular waves in premixed gas flames
    • H. PEARLMAN AND P. RONNEY, Self organized spiral and circular waves in premixed gas flames, J. Chem. Phys., 101 (1994), pp. 2632-2633.
    • (1994) J. Chem. Phys. , vol.101 , pp. 2632-2633
    • Pearlman, H.1    Ronney, P.2
  • 49
    • 0000738501 scopus 로고    scopus 로고
    • Overview: Nonlinear dynamics related to polymeric systems
    • I. R. EPSTEIN AND J. A. POJMAN, Overview: Nonlinear dynamics related to polymeric systems, Chaos, 9 (1999), pp. 255-259.
    • (1999) Chaos , vol.9 , pp. 255-259
    • Epstein, I.R.1    Pojman, J.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.