Rippling rectangular waves for a modified Benney equation

DOI10.1007/s13160-018-0304-1zbMath1406.35333OpenAlexW2803013990MaRDI QIDQ1756741

Ayuki Sekisaka, Toshiyuki Ogawa, Tomoyuki Miyaji

Publication date: 21 December 2018

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13160-018-0304-1

zbMATH Keywords

Benney equationmodified KdV equationtorus bifurcationrectangular traveling wave

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Spectral theory and eigenvalue problems for partial differential equations (35P99) Stability problems for infinite-dimensional dissipative dynamical systems (37L15) Bifurcations in context of PDEs (35B32) Traveling wave solutions (35C07)

Uses Software

• Matplotlib
• Torcont

Cites Work

• A codimension two bifurcation with a third order Picard-Fuchs equation
• Abelian integrals and bifurcation theory
• Geometric singular perturbation theory for ordinary differential equations
• Travelling wave solutions to a perturbed Korteweg-de Vries equation
• Absolute and convective instabilities of waves on unbounded and large bounded domains
• On the structure of the spectra of periodic travelling waves
• Numerical computation of the normal behaviour of invariant curves ofn-dimensional maps
• Exponential integrators
• Pulse Dynamics in an Unstable Medium
• Numerical Methods for Bifurcations of Dynamical Equilibria
• Continuation of Quasi-periodic Invariant Tori
• Elements of applied bifurcation theory

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