2022/03/23 by Handan Borluk, Gabriele Bruell, Dag Nilsson · 9 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Bifurcation #Characteristic equation #Geometry #Instability #Kadomtsev–Petviashvili equation #Line (geometry) #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Optics #Partial differential equation #Physics #Quantum mechanics #Stability (learning theory) #Transverse plane #Wavenumber
paper · doi:10.1111/sapm.12494
published in Studies in Applied Mathematics 149(1), 95-123 (Wiley)
openalex publication_date 2022/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract Of concern are traveling wave solutions for the fractional Kadomtsev–Petviashvili (fKP) equation. The existence of periodically modulated solitary wave solutions is proved by dimension‐breaking bifurcation. Moreover, the line solitary wave solutions and their transverse (in)stability are discussed. Analogous to the classical Kadmomtsev–Petviashvili (KP) equation, the fKP equation comes in two versions: fKP‐I and fKP‐II. We show that the line solitary waves of fKP‐I equation are transversely linearly instable. We also perform numerical experiments to observe the (in)stability dynamics of line solitary waves for both fKP‐I and fKP‐II equations.