Stability of travelling waves to Korteweg--de Vries type equations with fractional dispersion

2024/06/29 by Kaito Kokubu, Kokubu, Kaito · 1 citation
Mathematics · Physics and Astronomy · #35B53 #35C07 #35Q53 #35R11 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2407.00321

openalex publication_date 2024/06/29 · openalex created_date 2024/07/03 · openalex updated_date 2026/07/28

Abstract

We study stability of travelling wave solutions to Korteweg--de Vries type equations which has the fractional dispersion and integer-indices double power nonlinearities. It may depend on parity combinations of the two indices and the strength of dispersion whether these equations have a ground state solution. Therefore, we observe the stability phenomena on travelling wave solutions from the perspective of the parities and the dispersion, and we give the classification of phenomena on travelling wave solutions. In this paper, we focus on stable travelling wave solutions.

Cited by

• Classification of unstable travelling wave solutions to KdV type equations

Related

• Classification of unstable travelling wave solutions to KdV type equations
• Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
• Stability and instability of solitary waves of Korteweg-de Vries type
• Stability of Small Periodic Waves in Fractional KdV Type Equations
• Wave Dispersion in the Linearised Fractional Korteweg - de Vries equation