Nontivial solitary waves of GKP equation in multi-dimensional spaces

• Autores: Benjin Xuan
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 37, Nº. 1, 2003, págs. 11-23
• Idioma: inglés
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• Resumen

  • In this paper, using the Mountain Pass Lemma without (PS) con-dition due to Ambrosetti and Rabinowitz, we obtain the existence of the non-trivial solitary waves of Generalized Kadomtsev-Petviashvili equation in multi-dimensional spaces and for superlinear nonlinear term f (u) which satisfies some growth condition. By the Pohozaev type variational identity, we obtain the nonexistence of the nontrivial solitary waves for power function nonlinear case, i.e. f (u) = up where p 2(2n - 1)/(2n - 3).