We consider the orbital stability of line solitons of the Kadomtsev-Petviashvili-I equation in R × (R/2πZ). Zakharov  and Rousset-Tzvetkov  proved the orbital instability of the line solitons of the Kadomtsev-Petviashvili-I equation on R2. The orbital instability of the line solitons on R × (R/2πZ) with the traveling speed c > √43 was proved by Rousset-Tzvetkov  and the orbital stability of the line solitons with the traveling speed 0 < c < √43 was showed in . In this paper, we prove the orbital stability of the line soliton of the Kadomtsev-Petviashvili-I equation on R × (R/2πZ) with the critical speed c = √3 4 and the Zaitsev solitons near the line soliton. Since the linearized operator around the line soliton with the traveling speed √43 is degenerate, we cannot apply the argument in [32, 33, 34]. To prove the stability, we investigate the branch of the Zaitsev solitons and apply the argument .
|Number of pages||20|
|Journal||Differential and Integral Equations|
|Publication status||Published - Sep 2020|
All Science Journal Classification (ASJC) codes
- Applied Mathematics