Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011
Instability and patterns. Issue dedicated to the memory of A. Golovin
Page(s) 188 - 208
DOI https://doi.org/10.1051/mmnp/20116110
Published online 09 June 2010
  1. D. Casini, G. D’Alessandro, A. Politi. Soft turbulence in multimode lasers. Phys. Rev. A, 55 (1997), 751–760. [CrossRef]
  2. S. Chávez Cerda, S.B. Cavalcanti, J.M. Hickmann. A variational approach of nonlinear dissipative pulse propagation. Eur. Phys. J. D, 1 (1998), 313–316. [CrossRef] [EDP Sciences]
  3. P. Coullet, S. Fauve. Propagative phase dynamics for systems with Galilean invariance. Phys. Rev. Lett., 55 (1985), 2857–2859. [CrossRef] [PubMed]
  4. P. Coullet, G. Iooss. Instabilities of one-dimensional cellular patterns. Phys. Rev. Lett., 64 (1990), 866–869. [CrossRef] [MathSciNet] [PubMed]
  5. S.M. Cox, P.C. Matthews. Instability and localisation of patterns due to a conserved quantity. Physica D, 175 (2003), 196–219. [CrossRef] [MathSciNet]
  6. A.A. Golovin, S.H. Davis, P.W. Voorhees. Self-organization of quantum dots in epitaxially strained solid films. Phys. Rev. E, 68 (2003), 056203. [CrossRef]
  7. A.A. Golovin, Y. Kanevsky, A.A. Nepomnyashchy. Feedback control of subcritical Turing instability with zero mode. Phys. Rev. E, 79 (2009), 046218. [CrossRef] [MathSciNet]
  8. A.A. Golovin, A.A. Nepomnyashchy. Feedback control of subcritical oscillatory instabilities. Phys. Rev. E, 73 (2006), 046212. [CrossRef] [MathSciNet]
  9. A.A. Golovin, A.A. Nepomnyashchy, L.M. Pismen. Interaction between short-scale Marangoni convection and long-scale deformational instability. Phys. Fluids, 6 (1994), 34–47. [CrossRef] [MathSciNet]
  10. A.A. Golovin, A.A. Nepomnyashchy, L.M. Pismen. Nonlinear evolution and secondary instabilities of Marangoni convection in a liquid-gas system with deformable interface. J. Fluid Mech., 341 (1997), 317–341. [CrossRef] [MathSciNet]
  11. Y. Kanevsky, A.A. Nepomnyashchy. Stability and nonlinear dynamics of solitary waves generated by subcritical oscillatory instability under the action of feedback control. Phys. Rev. E, 76 (2007), 066305. [CrossRef] [MathSciNet]
  12. Y. Kanevsky, A.A. Nepomnyashchy. Dynamics of solitary waves generated by subcritical instabiity under the action of delayed feedback control. Physica D, (2009), DOI: 10.1016/j.physd.2009.10.007.
  13. N. Komarova, A.C. Newell. Nonlinear dynamics of sandbanks and sandwaves. J. Fluid Mech., 415 (2000), 285–321. [CrossRef] [MathSciNet]
  14. B.A. Malomed. Variational methods in nonlinear fiber optics and related fields. Progress in Optics, 43 (2002), 69–191.
  15. P.C. Matthews, S.M. Cox. One-dimensional pattern formation with Galilean invariance near a stationary bifurcation. Phys. Rev. E, 62 (2000), R1473–R1476. [CrossRef]
  16. P.C. Matthews, S.M. Cox. Pattern formation with a conservation law. Nonlinearity, 13 (2000), 1293–1320. [CrossRef] [MathSciNet]
  17. A.A. Nepomnyashchy, A.A. Golovin, V. Gubareva, V. Panfilov. Global feedback control of a long-wave morphological instability. Physica D, 199 (2004), 61–81. [CrossRef] [MathSciNet]
  18. A.C. Newell, J.A. Whitehead. Finite amplitude convection. J. Fluid Mech., 38 (1969), 279–303. [CrossRef]
  19. B.Y. Rubinstein, A.A. Nepomnyashchy, A.A. Golovin. Stability of localized solutions in a subcritically unstable pattern-forming system under a global delayed control. Phys. Rev. E, 75 (2007), 046213. [CrossRef] [MathSciNet]
  20. W. Schöpf, L. Kramer. Small-amplitude periodic and chaotic solutions of the complex Ginzburg-Landau equation for a subcritical bifurcation. Phys. Rev. Lett., 66 (1991), 2316–2319. [CrossRef] [PubMed]
  21. M. Sheintuch, O. Nekhamkina. Analysis of front interaction and control in stationary patterns of reaction-diffusion systems. Phys. Rev. E, 63 (2001), 056120. [CrossRef]
  22. V. Skarka, N.B. Aleksić. Stability criterion for dissipative soliton solutions of the one-, two-, and three-dimensional complex cubic-quintic Ginzburg-Landau equations. Phys. Rev. Lett., 96 (2006), 013903. [CrossRef] [PubMed]
  23. L.G. Stanton, A.A. Golovin. Global feedback control for pattern-forming systems. Phys. Rev. E, 76 (2007), 036210. [CrossRef] [MathSciNet]
  24. E.N. Tsoy, A. Ankiewicz, N. Akhmediev. Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation. Phys. Rev. E, 73 (2006), 036621. [CrossRef]

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