Ground State Solution for Schrödinger–KdV System with Periodic Potential

• Fei-Fei Liang ^[1] ; Xing-Ping Wu ^[1] ; Chun-Lei Tang ^[1]
  1. [1] Southwest University

     Southwest University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we study the coupled nonlinear Schrödinger–Korteweg–de Vries system with periodic potential. By using the variational method and Nehari manifold, we obtain the existence of non-trivial ground state solution.

• Referencias bibliográficas
  • 1. Ardila, A.H.: Existence and stability of a two-parameter family of solitary waves for a logarithmic NLS–KdV system. Nonlinear Anal. 189,...
  • 2. Bi, W.-J., Tang, C.-L.: Ground state solutions for a non-autonomous nonlinear Schrödinger–KdV system. Front. Math. China 15, 851–866 (2020)
  • 3. Bartsch, T., Ding, Y.: On a nonlinear Schrödinger equation with periodic potential. Math. Ann. 313, 15–37 (1999)
  • 4. Colorado, E.: Existence of bound and ground states for a system of coupled nonlinear Schrödinger–KdV equations. C. R. Math. Acad. Sci....
  • 5. Colorado, E.: On the existence of bound and ground states for some coupled nonlinear Schrödinger– Korteweg–de Vries equations. Adv. Nonlinear...
  • 6. Coti Zelati, V., Rabinowitz, P.H.: Homoclinic type solutions for a semilinear elliptic PDE on RN . Commun. Pure Appl. Math. 45, 1217–1269...
  • 7. Dias, J.-P., Mário, F., Filipe, O.: Existence of bound states for the coupled Schrödinger–KdV system with cubic nonlinearity. C. R. Math....
  • 8. Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)
  • 9. Kawahara, T., Sugimoto, N., Kakutani, T.: Nonlinear interaction between short and long capillarygravity waves. J. Phys. Soc. Jpn. 39, 1379–1386...
  • 10. Kryszewski, W., Szulkin, A.: Generalized linking theorem with an application to semilinear Schrödinger equation. Adv. Differ. Equ. 3,...
  • 11. Liu, C.-G., Zheng, Y.-Q.: On soliton solutions to a class of Schrödinger–KdV systems. Proc. Am. Math. Soc. 141, 3477–3484 (2013)
  • 12. Liao, F., Zhang, L.-M.: High accuracy split-step finite difference method for Schrödinger–KdV equations. Commun. Theort. Phys. 70, 413–422...
  • 13. Liang, F.-F., Wu, X.-P., Tang, C.-L.: Normalized Ground-State Solution for the Schrödinger–KdV System. Mediterr. J. Math. 19, 1–15 (2022)
  • 14. Liu, J., Liao, J.-F., Tang, C.-L.: A positive ground state solution for a class of asymptotically periodic Schrödinger equations. Comput....
  • 15. Willem, M.: Minimax Theorems. Birkhäuser, Basel (1996)
  • 16. Pankov, A.: Periodic nonlinear Schrödinger equation with application to photonic crystals. Milan J. Math. 73, 259–287 (2005)