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Nontrivial solitary waves of GKP equation in multi-dimensional spaces
Keywords:
Mountain Pass Lemma, Solitary wave, Generalized Kadomtsev-Petviashvili equation, 2000 Mathematics Subject Classification, Primary: 35J60 (en)Downloads
Abstract. In this paper, using the Mountain Pass Lemma without (PS) condition due to Ambrosetti and Rabinowitz, we obtain the existence of the nontrivial solitary waves of Generalized Kadomtsev-Petviashvili equation in multidimensional 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).
References
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