Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012
Solitary waves
Page(s) 13 - 31
DOI https://doi.org/10.1051/mmnp/20127202
Published online 29 February 2012
  1. N. Boussaid, S. Cuccagna. On stability of standing waves of nonlinear Dirac equations. ArXiv e-prints 1103.4452, (2011). [Google Scholar]
  2. V. S. Buslaev, G. S. Perel'an. Scattering for the nonlinear Schrödinger equation : states that are close to a soliton. St. Petersburg Math. J., 4 (1993), 1111–1142. [MathSciNet] [Google Scholar]
  3. V. S. Buslaev, C. Sulem. On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), 419–475. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Chugunova. Spectral stability of nonlinear waves in dynamical systems (Doctoral Thesis). McMaster University, Hamilton, Ontario, Canada, 2007. [Google Scholar]
  5. S. Cuccagna, T. Mizumachi. On asymptotic stability in energy space of ground states for nonlinear Schrödinger equations. Comm. Math. Phys., 284 (2008), 51–77. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Comech. On the meaning of the Vakhitov-Kolokolov stability criterion for the nonlinear Dirac equation. ArXiv e-prints, (2011), arXiv :1107.1763. [Google Scholar]
  7. S. Cuccagna. Stabilization of solutions to nonlinear Schrödinger equations. Comm. Pure Appl. Math., 54 (2001), 1110–1145. [CrossRef] [MathSciNet] [Google Scholar]
  8. T. Cazenave, L. Vázquez. Existence of localized solutions for a classical nonlinear Dirac field. Comm. Math. Phys., 105 (1986), 35–47. [CrossRef] [MathSciNet] [Google Scholar]
  9. G. H. Derrick. Comments on nonlinear wave equations as models for elementary particles. J. Mathematical Phys., 5 (1964), 1252–1254. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. J. Gross, A. Neveu. Dynamical symmetry breaking in asymptotically free field theories. Phys. Rev. D, 10 (1974), 3235–3253. [CrossRef] [Google Scholar]
  11. V. Georgiev, M. Ohta. Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations. ArXiv e-prints, (2010). [Google Scholar]
  12. M. Grillakis. Linearized instability for nonlinear Schrödinger and Klein-Gordon equations. Comm. Pure Appl. Math., 41 (1988), 747–774. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Gross. The Cauchy problem for the coupled Maxwell and Dirac equations. Comm. Pure Appl. Math., 19 (1966), 1–15. [CrossRef] [MathSciNet] [Google Scholar]
  14. M. Grillakis, J. Shatah, W. Strauss. Stability theory of solitary waves in the presence of symmetry. I. J. Funct. Anal., 74 (1987), 160–197. [CrossRef] [MathSciNet] [Google Scholar]
  15. S. Y. Lee, A. Gavrielides. Quantization of the localized solutions in two-dimensional field theories of massive fermions. Phys. Rev. D, 12 (1975), 3880–3886. [CrossRef] [Google Scholar]
  16. D. E. Pelinovsky, A. Stefanov. Asymptotic stability of small gap solitons in the nonlinear Dirac equations. ArXiv e-prints, (2010), arXiv :1008.4514. [Google Scholar]
  17. J. Shatah. Stable standing waves of nonlinear Klein-Gordon equations. Comm. Math. Phys., 91 (1983), 313–327. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Shatah. Unstable ground state of nonlinear Klein-Gordon equations. Trans. Amer. Math. Soc., 290 (1985), 701–710. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Soler. Classical, stable, nonlinear spinor field with positive rest energy. Phys. Rev. D, 1 (1970), 2766–2769. [CrossRef] [Google Scholar]
  20. J. Shatah, W. Strauss. Instability of nonlinear bound states. Comm. Math. Phys., 100 (1985), 173–190. [CrossRef] [MathSciNet] [Google Scholar]
  21. A. Soffer, M. I. Weinstein. Multichannel nonlinear scattering for nonintegrable equations. II. The case of anisotropic potentials and data. J. Differential Equations, 98 (1992), 376–390. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Soffer, M. I. Weinstein. Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations. Invent. Math., 136 (1999), 9–74. [CrossRef] [MathSciNet] [Google Scholar]
  23. N. G. Vakhitov, A. A. Kolokolov. Stationary solutions of the wave equation in the medium with nonlinearity saturation. Radiophys. Quantum Electron., 16 (1973), 783–789. [CrossRef] [Google Scholar]
  24. M. I. Weinstein. Modulational stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal., 16 (1985), 472–491. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. I. Weinstein. Lyapunov stability of ground states of nonlinear dispersive evolution equations. Comm. Pure Appl. Math., 39 (1986), 51–67. [CrossRef] [MathSciNet] [Google Scholar]
  26. V. Zakharov. Instability of self-focusing of light. Zh. Éksp. Teor. Fiz, 53 (1967), 1735–1743. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.