Nonlinear internal dynamics of the double-sine-Gordon soliton

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Abstract
We have investigated the nonlinear internal dynamics of the double-sine-Gordon soliton using the recently developed collective-variable Hamiltonian formalism. We have carried out this investigation in the approximation in which the continuum phonon field is neglected. In order to test the range of validity of this approximation, we carried out a similar study using molecular-dynamics simulations of the double-sine-Gordon equation. A detailed comparison of the results yields an excellent agreement of the frequencies, amplitudes, and spatial shapes of the internal modes between the simulations and the Hamiltonian calculations. This agreement holds over a wide range of amplitude, from small oscillations to the highly nonlinear large-oscillation regime. The agreement supports the view that the coupling of the internal oscillations of the double-sine-Gordon soliton to the phonon continuum is extremely weak and can be neglected, even when the internal oscillation is highly nonlinear.