Transverse spectral Instabilities in rotation-modified Kadomtsev-Petviashvili equation and related models

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Main Authors: Bhavna, Pandey, Ashish Kumar, Semenova, Anastassiya
Format: Preprint
Published: 2023
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author Bhavna
Pandey, Ashish Kumar
Semenova, Anastassiya
author_facet Bhavna
Pandey, Ashish Kumar
Semenova, Anastassiya
contents The rotation modified Kadomtsev Petviashvili equation which is also known as the Kadomtsev Petviashvili Ostrovsky equation, describes the gradual wave field diffusion in the transverse direction to the direction of the propagation of the wave in a rotating frame of reference. This equation is a generalization of the Ostrovsky equation additionally having weak transverse effects. We investigate transverse instability and stability of small periodic traveling waves of the Ostrovsky equation with respect to either periodic or square integrable perturbations in the direction of wave propagation and periodic perturbations in the transverse direction of motion in the rotation modified Kadomtsev Petviashvili equation. We also study transverse stability or instability in generalized rotation modified KP equation by taking dispersion term as general and quadratic and cubic nonlinearity. As a consequence, we obtain transverse stability or instability in two-dimensional generalization of RMBO equation, Ostrovsky-Gardner equation, Ostrovsky-fKdV equation, Ostrovsky-mKdV equation, Ostrovsky-ILW equation, Ostrovsky-Whitham etc.
format Preprint
id arxiv_https___arxiv_org_abs_2305_10700
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Transverse spectral Instabilities in rotation-modified Kadomtsev-Petviashvili equation and related models
Bhavna
Pandey, Ashish Kumar
Semenova, Anastassiya
Analysis of PDEs
The rotation modified Kadomtsev Petviashvili equation which is also known as the Kadomtsev Petviashvili Ostrovsky equation, describes the gradual wave field diffusion in the transverse direction to the direction of the propagation of the wave in a rotating frame of reference. This equation is a generalization of the Ostrovsky equation additionally having weak transverse effects. We investigate transverse instability and stability of small periodic traveling waves of the Ostrovsky equation with respect to either periodic or square integrable perturbations in the direction of wave propagation and periodic perturbations in the transverse direction of motion in the rotation modified Kadomtsev Petviashvili equation. We also study transverse stability or instability in generalized rotation modified KP equation by taking dispersion term as general and quadratic and cubic nonlinearity. As a consequence, we obtain transverse stability or instability in two-dimensional generalization of RMBO equation, Ostrovsky-Gardner equation, Ostrovsky-fKdV equation, Ostrovsky-mKdV equation, Ostrovsky-ILW equation, Ostrovsky-Whitham etc.
title Transverse spectral Instabilities in rotation-modified Kadomtsev-Petviashvili equation and related models
topic Analysis of PDEs
url https://arxiv.org/abs/2305.10700