Analytical and Numerical Results on Global Dynamics of the Generalized Boussinesq Equation with Cubic Nonlinearity and External Excitation

Abstract

This paper analytically and numerically presents global dynamics of the generalized Boussinesq equation (GBE) with cubic nonlinearity and harmonic excitation. The effect of the damping coefficient on the dynamical responses of the generalized Boussinesq equation is clearly revealed. Using the reductive perturbation method, an equivalent wave equation is then derived from the complex nonlinear equation of the GBE. The persistent homoclinic orbit for the perturbed equation is located through the first and second measurements, and the breaking of the homoclinic structure will generate chaos in a Smale horseshoe sense for the GBE. Numerical examples are used to test the validity of the theoretical prediction. Both theoretical prediction and numerical simulations demonstrate the homoclinic chaos for the GBE.

Analysis of perturbed Boussinesq equation via novel integrating schemes

“…PBE model has attracted the attention of many researchers. In [22] the perturbed Boussinesq equation is investigated using generalized Kudryashov method and sine-Gordon expansion method. A study is also conducted on new perturbed conformable Boussinesq-like equations to deduce soliton solutions [23].…”