Solitary‐wave propagation and interactions for a sixth‐order generalized Boussinesq equation

Abstract

We study the solitary waves and their interaction for a six-order generalized Boussinesq equation (SGBE) both numerically and analytically. A shooting method with appropriate initial conditions, based on the phase plane analysis around the equilibrium point, is used to construct the solitary-wave solutions for this nonintegrable equation. A symmetric three-level implicit finite difference scheme with a free parameter θ is proposed to study the propagation and interactions of solitary waves. Numerical simulations show the propagation of a single solitary wave of SGBE, and two solitary waves pass by each other without changing their shapes in the head-on collisions

Exact periodic solutions of the sixth-order generalized Boussinesq equation

“…The simple transformations, x → x; t → t and u → u/2, reduce equation (1.4) to (1.1) with the parameter α = 2/5. Kawahara et al [13] studied the solitary waves and their interactions for the above equation (1.4). They seek traveling wave solutions numerically and find that in contrast to the BE, the SGBE admits solitary-wave solutions for a narrow range of variation of the phase velocity (i.e.…”

The Limit Behavior of Solutions for the Cauchy Problem of the Sixth-Order Boussinesq Equation

“…Maugin [16] also proposed (1.1) in modeling the nonlinear lattice dynamics in elastic crystals. Kawahara et al [13] studied the solitary waves and their interactions for the above equation (1.1) (see also [7]).…”

Exact controllability and stability of the Sixth Order Boussinesq equation

“…The sixth order Boussinesq equation was also proposed in modeling the nonlinear lattice dynamics in elastic crystals by Maugin [16]. In addition, Feng et al [8] studied the solitary waves as well as their interactions of the sixth order Boussiensq equation. Kamenov [11] obtained an exact periodic solution through the Hirota's bilinear transform method.…”