Wobbling Fractals for The Double Sine–Gordon Equation

This paper studies a perturbative approach for the double sine–Gordon equation. Following this path, we are able to obtain system of differential equations that shows amplitude and phase modulation approximate solution. In case λ = 0, get well-known perturbation theory For special value −1/8, derive phase-locked solution with same frequency linear case. general, both coherent (solitary waves, lumps so on) solutions as well fractal solutions. Using symmetry considerations, can demonstrate existence envelope wobbling solitary due critical observation depending on position. Because equation has very rich behavior, including chaotic an arbitrary function in its solution, main conclusion is it too reductive focus only