Spectral analysis of the periodic b-KP equation under transverse perturbations

The b -family-Kadomtsev–Petviashvili equation ( b -KP) is a two dimensional generalization of the b -family equation. In this paper, we study the spectral stability of the one-dimensional small-amplitude periodic traveling waves with respect to two-dimensional perturbations which are either co-perio...

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Bibliographic Details
Published inMathematische annalen Vol. 390; no. 4; pp. 6315 - 6354
Main Authors Chen, Robin Ming, Fan, Lili, Wang, Xingchang, Xu, Runzhang
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024
Springer Nature B.V
Subjects
Longitudinal waves
Mathematics
Mathematics and Statistics
Parameters
Perturbation
Spectrum analysis
Stability analysis
Stability criteria
Traveling waves
Two dimensional analysis
Wave dispersion
Wave propagation
37K45
35B35
35C07
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Summary:The b -family-Kadomtsev–Petviashvili equation ( b -KP) is a two dimensional generalization of the b -family equation. In this paper, we study the spectral stability of the one-dimensional small-amplitude periodic traveling waves with respect to two-dimensional perturbations which are either co-periodic in the direction of propagation, or nonperiodic (localized or bounded). We perform a detailed spectral analysis of the linearized problem associated to the above mentioned perturbations, and derive various stability and instability criteria which depends in a delicate way on the parameter value of b , the transverse dispersion parameter σ , and the wave number k of the longitudinal waves.
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content type line 14
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-024-02907-8