Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 79
Number of page(s) 31
DOI https://doi.org/10.1051/cocv/2024065
Published online 07 October 2024
  1. W.A. Strauss, Existence of solitary waves in higher dimensions. Commun. Math. Phys. 55 (1977) 149–162. [CrossRef] [Google Scholar]
  2. H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state. Arch. Rational Mech. Anal. 82 (1983) 313–345. [CrossRef] [MathSciNet] [Google Scholar]
  3. T. Cazenave and P.-L. Lions, Orbital stability of standing waves for some nonlinear Schrodinger equations. Commun. Math. Phys. 85 (1982) 549-561 [CrossRef] [Google Scholar]
  4. H. Berestycki and T. Cazenave, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein- Gordon non linéaires. C. R. Acad. Sci. Paris 293 (1981) 489–492. [Google Scholar]
  5. P. Kfoury, S. Le Coz and T.-P. Tsai, Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation. C. R., Math., Acad. Sci. Paris 360 (2022) 867–892. [CrossRef] [MathSciNet] [Google Scholar]
  6. F.J. Liu, T.-P. Tsai and I. Zwiers, Existence and stability of standing waves for one dimensional NLS with triple power nonlinearities. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 211 (2021) 34. [Google Scholar]
  7. T. Morrison and T.-P. Tsai, On standing waves of 1d nonlinear Schrödinger equation with triple power nonlinearity. arXiv2312.03693 (2023). [Google Scholar]
  8. G. Rowlands, On the stability of solutions of the non-linear Schrödinger equation. IMA J. Appl. Math. 13 (1974) 367–377. [CrossRef] [Google Scholar]
  9. T. Gallay and M. Hǎrǎgus, Orbital stability of periodic waves for the nonlinear Schrödinger equation. J. Dynam. Differ. Eq. 19 (2007) 825–865. [CrossRef] [Google Scholar]
  10. T. Gallay and M. Hărăguş, Stability of small periodic waves for the nonlinear Schrödinger equation. J. Differ. Eq. 234 (2007) 544–581. [CrossRef] [Google Scholar]
  11. N. Bottman, B. Deconinck and M. Nivala, Elliptic solutions of the defocusing NLS equation are stable. J. Phys. A 44 (2011) 285201. [CrossRef] [MathSciNet] [Google Scholar]
  12. B. Deconinck and B. L. Segal, The stability spectrum for elliptic solutions to the focusing NLS equation. Physica D 346 (2017) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  13. B. Deconinck and J. Upsal, The orbital stability of elliptic solutions of the focusing nonlinear Schrödinger equation. SIAM J. Math. Anal. 52 (2020) 1–41. [CrossRef] [MathSciNet] [Google Scholar]
  14. T. Gallay and D. Pelinovsky, Orbital stability in the cubic defocusing NLS equation: II. The black soliton. J. Differ. Eq. 258 (2015) 3639–3660. [CrossRef] [Google Scholar]
  15. J. Chen and D.E. Pelinovsky, Rogue periodic waves of the focusing nonlinear Schrödinger equation. Proc. R. Soc. Lond., A Math. Phys. Eng. Sci. 474 (2018) 18. [Google Scholar]
  16. S. Gustafson, S. Le Coz and T.-P. Tsai, Stability of periodic waves of 1D cubic nonlinear Schrödinger equations. Appl. Math. Res. Express. 2 (2017) 431–487. [CrossRef] [Google Scholar]
  17. G. Alves and F. Natali, Periodic waves for the cubic-quintic nonlinear Schrödinger equation: existence and orbital stability. Discrete Contin. Dyn. Syst., Ser. B 28 (2023) 854–871. [CrossRef] [MathSciNet] [Google Scholar]
  18. G.E.B. Moraes and G. de Loreno, Cnoidal waves for the quintic Klein-Gordon and Schrödinger equations: existence and orbital instability. J. Math. Anal. Appl. 513 (2022) 22. [Google Scholar]
  19. M. Hayashi, Long-period limit of exact periodic traveling wave solutions for the derivative nonlinear Schrödinger equation. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 36 (2019) 1331–1360. [CrossRef] [MathSciNet] [Google Scholar]
  20. K.P. Leisman, J.C. Bronski, M.A. Johnson and R. Marangell, Stability of traveling wave solutions of nonlinear dispersive equations of NLS type. Arch. Ration. Mech. Anal. 240 (2021) 927–969. [CrossRef] [MathSciNet] [Google Scholar]
  21. T. Cazenave, Semilinear Schrödinger equations. Vol. 10 of Courant Lecture Notes in Mathematics. New York University/Courant Institute of Mathematical Sciences, New York (2003). [Google Scholar]
  22. A. Szulkin and T. Weth, The method of Nehari manifold, in Handbook of Nonconvex Analysis and Applications. International Press, Somerville, MA (2010) 597–632. [Google Scholar]
  23. A. Pankov, Gap solitons in periodic discrete nonlinear schrodinger equations. II. A generalized Nehari manifold approach. Discrete Continuous Dyn. Syst. 19 (2017) 419. [Google Scholar]
  24. G. Zhang and A. Pankov, Standing waves of the discrete nonlinear Schrödinger equations with growing potentials. Commun. Math. Anal. 5 (2008) 38–49. [MathSciNet] [Google Scholar]
  25. M. Hayashi, Potential well theory for the derivative nonlinear Schrödinger equation. Anal. PDE 14 (2021) 909–944. [CrossRef] [MathSciNet] [Google Scholar]
  26. M. Colin and T. Watanabe, On the existence of ground states for a nonlinear klein-gordon-maxwell type system. Funkcialaj Ekvacioj 61 (2018) 1–14. [CrossRef] [MathSciNet] [Google Scholar]

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