Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equations

Authors

  • University of Dayton
  • University of Dayton

Abstract

We consider the damped externally excited KdV and BBM equations and use an asymptotic perturbation method to analyze the stability of solutions. We consider the primary resonance by defining the detuning parameter. External-excitation and frequency-response curves are shown to exhibit jump and hysteresis phenomena (dis-continuous transitions between two stable solutions) for both KdV and BBM equations.

Published

2012-03-20

Issue

Section

Articles

How to Cite

Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equations. (2012). Nonlinear Studies, 19(2). https://nonlinearstudies.com/index.php/nonlinear/article/view/442