Travelling fronts in a piecewise-linear bistable system

Nonlinearity

Volumn 16, Issue 1, 2003, Pages 313-325

  Bakanas, R ^a  

^a CENTER FOR PHYSICAL SCIENCES AND TECHNOLOGY   (Lithuania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041791308     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/1/319     Document Type: Article

References (27)

1. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
2. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
3. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
4. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
5. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
6. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
7. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
8. Meron E 1992 Pattern formation in excitable media Phys. Rep. 218 1-66 Cross M C and Hohenberg P S 1993 Pattern formation outside the equilibrium Rev. Mod. Phys. 65 851-1112 Kapral R and Showalter K (ed) 1994 Chemical Waves and Patterns (Dordrecht: Kluwer) Niedernostheide F J (ed) 1995 Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices (Berlin: Springer) Buka A and Kramer L (ed) 1996 Pattern Formation in Liquid Crystals (New York: Springer) Bowman C and Newell A C 1998 Natural patterns and wavelets Rev. Mod. Phys. 70 289-302 Ermentrout B 1998 Electrophysics of nerve fiber Rep. Prog. Phys. 61 353-430 Ben-Jacob E, Cohen I and Levine H 2000 Cooperative self-organization of microorganisms Adv. Phys. 49 395-554
9. Ebert U and van Saarloos W 2000 Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts Physica D 146 1-99 Fort J and Mendez V 2002 Wave front in time-delayed reaction-diffusion systems. Theory and comparison to experiment Rep. Prog. Phys. 65 895-954
10. Ebert U and van Saarloos W 2000 Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts Physica D 146 1-99 Fort J and Mendez V 2002 Wave front in time-delayed reaction-diffusion systems. Theory and comparison to experiment Rep. Prog. Phys. 65 895-954
11. Dee G and Langer J S 1983 Propagating pattern selection Phys. Rev. Lett. 50 383-6 Ben-Jackob E, Brand H R, Dee G, Kramer L and Langer J S 1985 Pattern propagation in nonlinear dissipative systems Physica D 14 348-64 Powell J A and Newell A C 1991 Competition between generic and nongeneric fronts in envelope equations Phys. Rev. A 44 3636-52 Paquette G C, Chen L-Y, Goldenfeld N and Ono Y 1994 Structural stability and renormalization group for propagating fronts Phys. Rev. Lett. 72 76-9 Kessler D A, Ner Z and Sander L M 1998 Front propagation: precursors, cuttoffs, and structural stability Phys. Rev. E 58 107-14 Chomaz J-M and Couairon A 2000 Propagating pattern selection and causality reconsidered Phys. Rev. Lett. 84 1910-13 Panja D and van Saarloos W 2002 The weakly pushed nature of 'pulled' fronts with a cutoff Phys. Rev. E 65 057202-(1-3)
12. Dee G and Langer J S 1983 Propagating pattern selection Phys. Rev. Lett. 50 383-6 Ben-Jackob E, Brand H R, Dee G, Kramer L and Langer J S 1985 Pattern propagation in nonlinear dissipative systems Physica D 14 348-64 Powell J A and Newell A C 1991 Competition between generic and nongeneric fronts in envelope equations Phys. Rev. A 44 3636-52 Paquette G C, Chen L-Y, Goldenfeld N and Ono Y 1994 Structural stability and renormalization group for propagating fronts Phys. Rev. Lett. 72 76-9 Kessler D A, Ner Z and Sander L M 1998 Front propagation: precursors, cuttoffs, and structural stability Phys. Rev. E 58 107-14 Chomaz J-M and Couairon A 2000 Propagating pattern selection and causality reconsidered Phys. Rev. Lett. 84 1910-13 Panja D and van Saarloos W 2002 The weakly pushed nature of 'pulled' fronts with a cutoff Phys. Rev. E 65 057202-(1-3)
13. Dee G and Langer J S 1983 Propagating pattern selection Phys. Rev. Lett. 50 383-6 Ben-Jackob E, Brand H R, Dee G, Kramer L and Langer J S 1985 Pattern propagation in nonlinear dissipative systems Physica D 14 348-64 Powell J A and Newell A C 1991 Competition between generic and nongeneric fronts in envelope equations Phys. Rev. A 44 3636-52 Paquette G C, Chen L-Y, Goldenfeld N and Ono Y 1994 Structural stability and renormalization group for propagating fronts Phys. Rev. Lett. 72 76-9 Kessler D A, Ner Z and Sander L M 1998 Front propagation: precursors, cuttoffs, and structural stability Phys. Rev. E 58 107-14 Chomaz J-M and Couairon A 2000 Propagating pattern selection and causality reconsidered Phys. Rev. Lett. 84 1910-13 Panja D and van Saarloos W 2002 The weakly pushed nature of 'pulled' fronts with a cutoff Phys. Rev. E 65 057202-(1-3)
14. Dee G and Langer J S 1983 Propagating pattern selection Phys. Rev. Lett. 50 383-6 Ben-Jackob E, Brand H R, Dee G, Kramer L and Langer J S 1985 Pattern propagation in nonlinear dissipative systems Physica D 14 348-64 Powell J A and Newell A C 1991 Competition between generic and nongeneric fronts in envelope equations Phys. Rev. A 44 3636-52 Paquette G C, Chen L-Y, Goldenfeld N and Ono Y 1994 Structural stability and renormalization group for propagating fronts Phys. Rev. Lett. 72 76-9 Kessler D A, Ner Z and Sander L M 1998 Front propagation: precursors, cuttoffs, and structural stability Phys. Rev. E 58 107-14 Chomaz J-M and Couairon A 2000 Propagating pattern selection and causality reconsidered Phys. Rev. Lett. 84 1910-13 Panja D and van Saarloos W 2002 The weakly pushed nature of 'pulled' fronts with a cutoff Phys. Rev. E 65 057202-(1-3)
15. Dee G and Langer J S 1983 Propagating pattern selection Phys. Rev. Lett. 50 383-6 Ben-Jackob E, Brand H R, Dee G, Kramer L and Langer J S 1985 Pattern propagation in nonlinear dissipative systems Physica D 14 348-64 Powell J A and Newell A C 1991 Competition between generic and nongeneric fronts in envelope equations Phys. Rev. A 44 3636-52 Paquette G C, Chen L-Y, Goldenfeld N and Ono Y 1994 Structural stability and renormalization group for propagating fronts Phys. Rev. Lett. 72 76-9 Kessler D A, Ner Z and Sander L M 1998 Front propagation: precursors, cuttoffs, and structural stability Phys. Rev. E 58 107-14 Chomaz J-M and Couairon A 2000 Propagating pattern selection and causality reconsidered Phys. Rev. Lett. 84 1910-13 Panja D and van Saarloos W 2002 The weakly pushed nature of 'pulled' fronts with a cutoff Phys. Rev. E 65 057202-(1-3)
16. Dee G and Langer J S 1983 Propagating pattern selection Phys. Rev. Lett. 50 383-6 Ben-Jackob E, Brand H R, Dee G, Kramer L and Langer J S 1985 Pattern propagation in nonlinear dissipative systems Physica D 14 348-64 Powell J A and Newell A C 1991 Competition between generic and nongeneric fronts in envelope equations Phys. Rev. A 44 3636-52 Paquette G C, Chen L-Y, Goldenfeld N and Ono Y 1994 Structural stability and renormalization group for propagating fronts Phys. Rev. Lett. 72 76-9 Kessler D A, Ner Z and Sander L M 1998 Front propagation: precursors, cuttoffs, and structural stability Phys. Rev. E 58 107-14 Chomaz J-M and Couairon A 2000 Propagating pattern selection and causality reconsidered Phys. Rev. Lett. 84 1910-13 Panja D and van Saarloos W 2002 The weakly pushed nature of 'pulled' fronts with a cutoff Phys. Rev. E 65 057202-(1-3)
17. Dee G and Langer J S 1983 Propagating pattern selection Phys. Rev. Lett. 50 383-6 Ben-Jackob E, Brand H R, Dee G, Kramer L and Langer J S 1985 Pattern propagation in nonlinear dissipative systems Physica D 14 348-64 Powell J A and Newell A C 1991 Competition between generic and nongeneric fronts in envelope equations Phys. Rev. A 44 3636-52 Paquette G C, Chen L-Y, Goldenfeld N and Ono Y 1994 Structural stability and renormalization group for propagating fronts Phys. Rev. Lett. 72 76-9 Kessler D A, Ner Z and Sander L M 1998 Front propagation: precursors, cuttoffs, and structural stability Phys. Rev. E 58 107-14 Chomaz J-M and Couairon A 2000 Propagating pattern selection and causality reconsidered Phys. Rev. Lett. 84 1910-13 Panja D and van Saarloos W 2002 The weakly pushed nature of 'pulled' fronts with a cutoff Phys. Rev. E 65 057202-(1-3)
18. Schlogl F, Escher C and Berry R S 1983 Fluctuations in the interface between two phases Phys. Rev. A 27 2698-704 Schimansky-Geier L and Zulicke Ch 1991 Kink propagation induced by multiplicative noise Z. Phys. B 82 157-62 Bass F G and Bakanas R 1996 Propagation of a Gunn wave under the influence of spatially homogeneous random perturbations Phys. Lett. A 214 301-6 Dziarmaga J and Zakrzewsky W 1998 What happens with the initially kicked soliton? Phys. Lett. A 242 227-32 Bass F G and Bakanas R 2000 Spatially localized autowave under spatio-temporal fluctuations Waves in Random Media 10 217-29
19. Schlogl F, Escher C and Berry R S 1983 Fluctuations in the interface between two phases Phys. Rev. A 27 2698-704 Schimansky-Geier L and Zulicke Ch 1991 Kink propagation induced by multiplicative noise Z. Phys. B 82 157-62 Bass F G and Bakanas R 1996 Propagation of a Gunn wave under the influence of spatially homogeneous random perturbations Phys. Lett. A 214 301-6 Dziarmaga J and Zakrzewsky W 1998 What happens with the initially kicked soliton? Phys. Lett. A 242 227-32 Bass F G and Bakanas R 2000 Spatially localized autowave under spatio-temporal fluctuations Waves in Random Media 10 217-29
20. Schlogl F, Escher C and Berry R S 1983 Fluctuations in the interface between two phases Phys. Rev. A 27 2698-704 Schimansky-Geier L and Zulicke Ch 1991 Kink propagation induced by multiplicative noise Z. Phys. B 82 157-62 Bass F G and Bakanas R 1996 Propagation of a Gunn wave under the influence of spatially homogeneous random perturbations Phys. Lett. A 214 301-6 Dziarmaga J and Zakrzewsky W 1998 What happens with the initially kicked soliton? Phys. Lett. A 242 227-32 Bass F G and Bakanas R 2000 Spatially localized autowave under spatio-temporal fluctuations Waves in Random Media 10 217-29
21. Schlogl F, Escher C and Berry R S 1983 Fluctuations in the interface between two phases Phys. Rev. A 27 2698-704 Schimansky-Geier L and Zulicke Ch 1991 Kink propagation induced by multiplicative noise Z. Phys. B 82 157-62 Bass F G and Bakanas R 1996 Propagation of a Gunn wave under the influence of spatially homogeneous random perturbations Phys. Lett. A 214 301-6 Dziarmaga J and Zakrzewsky W 1998 What happens with the initially kicked soliton? Phys. Lett. A 242 227-32 Bass F G and Bakanas R 2000 Spatially localized autowave under spatio-temporal fluctuations Waves in Random Media 10 217-29
22. Schlogl F, Escher C and Berry R S 1983 Fluctuations in the interface between two phases Phys. Rev. A 27 2698-704 Schimansky-Geier L and Zulicke Ch 1991 Kink propagation induced by multiplicative noise Z. Phys. B 82 157-62 Bass F G and Bakanas R 1996 Propagation of a Gunn wave under the influence of spatially homogeneous random perturbations Phys. Lett. A 214 301-6 Dziarmaga J and Zakrzewsky W 1998 What happens with the initially kicked soliton? Phys. Lett. A 242 227-32 Bass F G and Bakanas R 2000 Spatially localized autowave under spatio-temporal fluctuations Waves in Random Media 10 217-29
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