Planar and Radial Kinks in Nonlinear Klein-Gordon Models: Existence, Stability and Dynamics

Movies accompanying the paper:

Planar and Radial Kinks in Nonlinear Klein-Gordon Models: Existence, Stability and Dynamics.
P.G. Kevrekidis, I. Danaila, J.-G. Caputo, and R. Carretero-González.
Phys. Rev. E 98 (2018) 052217. PDF.

Animations depicting the dynamics ensuing from the dynamical evolution of sine-Gordon (sG) and φ⁴ kinks under the influence of the external potential A sech²(x).
The background image depicts the spatial evolution of the kink while the magenta line depicts the corresponding dynamics using our adiabatic invariant reduction.
Left column: sine-Gordon. Right column: φ⁴. Click on any image to get the movie.

Movie#1: [ mpeg ] sG kink for A=0.1 and perturbed along the k=2 mode.
Movie#5: [ mpeg ] φ⁴ kink for A=0.1 and perturbed along the k=2 mode.

Movie#2: [ mpeg ] sG kink for A=0.25 and perturbed along the k=2 mode.
Movie#6: [ mpeg ] φ⁴ kink for A=0.25 and perturbed along the k=2 mode.

Movie#3: [ mpeg ] sG kink for A=0 and perturbed along the k=2,4,6,8,10 modes.
Movie#7: [ mpeg ] φ⁴ kink for A=0 and perturbed along the k=2,4,6,8,10 modes.

Movie#4: [ mpeg ] sG kink for A=0.25 and perturbed along the k=2,4,6,8,10 modes.
Movie#8: [ mpeg ] φ⁴ kink for A=0.25 and perturbed along the k=2,4,6,8,10 modes.

Movie#1: [ mpeg ] sG kink for A=0.1 and perturbed along the k=2 mode.	Movie#5: [ mpeg ] φ⁴ kink for A=0.1 and perturbed along the k=2 mode.

Movie#2: [ mpeg ] sG kink for A=0.25 and perturbed along the k=2 mode.	Movie#6: [ mpeg ] φ⁴ kink for A=0.25 and perturbed along the k=2 mode.

Movie#3: [ mpeg ] sG kink for A=0 and perturbed along the k=2,4,6,8,10 modes.	Movie#7: [ mpeg ] φ⁴ kink for A=0 and perturbed along the k=2,4,6,8,10 modes.

Movie#4: [ mpeg ] sG kink for A=0.25 and perturbed along the k=2,4,6,8,10 modes.	Movie#8: [ mpeg ] φ⁴ kink for A=0.25 and perturbed along the k=2,4,6,8,10 modes.