Stability of the line soliton of the kadomtsev-petviashvili-i equation with the critical traveling speed

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the orbital stability of line solitons of the Kadomtsev-Petviashvili-I equation in R × (R/2πZ). Zakharov [40] and Rousset-Tzvetkov [31] 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 [32] and the orbital stability of the line solitons with the traveling speed 0 < c < 43 was showed in [34]. 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 [37].

Original languageEnglish
Pages (from-to)507-526
Number of pages20
JournalDifferential and Integral Equations
Volume33
Issue number9-10
Publication statusPublished - Sep 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Stability of the line soliton of the kadomtsev-petviashvili-i equation with the critical traveling speed'. Together they form a unique fingerprint.

Cite this