Dynamics of kink train solutions in deformed Multiple sine-Gordon models

Abstract

This paper examines the effects of a thin layer of inhomogeneity on periodic solutions of the Multiple-sine-Gordon (MsG) model. We investigate the dynamics of the perturbed Double-sine-Gordon (DsG) system as a significant and more practical case of such configurations. The thin barrier acts as a potential well (potential barrier) and causes critical deformations in kink train solutions and some basic properties of the periodic solutions, such as the type of sub-kinks, their amplitude, energy and wavelength. Stability of the initial kink chain during the interaction with medium defects is analyzed using their phase diagram. Sudden changes in the profile of kink trains due to the disruption of their amplitude and wavelength are considered. The time evolution of moving kink chain solutions while interacting with medium fractures is also studied.

Figures (12)

• Figure 1: (a) The DsG Potential. The dashed curve is for $\epsilon=10$, the dash-dotted curve is for $\epsilon=1$, and the solid curve is for $\epsilon=0$ (sG). (b) The MsG Potential for $N=5$. The dashed curve is for $\epsilon=10$, the dotted curve is for $\epsilon=1$ and the solid curve is for $\epsilon=0$ .
• Figure 2: Jacobi Elliptic Functions as a function of u for $k=0.99$.
• Figure 3: Single soliton solutions (a) For DsG with $\epsilon=10$ (dash-dotted curve) and $\epsilon=6$ (dashed curve) (b) The MsG system ($N=3$) with $\epsilon=10$ (dash-dotted curve) and $\epsilon=6$ (dashed curve) .
• Figure 4: (a) $\phi$ diagram as a function of $x$ for $N=2$ and $P= -0.009987500000000$; $\epsilon=10$ for $0 \leq x \leq x_{1}$, $x_{2} \leq x \leq 100$ and $\epsilon=5$ for $x_{1}<x<x_{2}$. For dotted, dash-dotted and solid curves $x_{1}=26.74, 28.01, 29.05$ and $x_{2}=40$ respectively. (b) $\phi$ diagram as a function of $x$ for $N=2$ and $P= -0.009987500000000$; $\epsilon=10$ for $0 \leq x \leq x_{1}$, $x_{2} \leq x \leq 100$ and $\epsilon=5$ for $x_{1}<x<x_{2}$. For dotted, dash-dotted, dashed and solid curves $x_{1}=30$ and $x_{2}$ are corresponded to $35, 40, 45$ and $50$ respectively.
• Figure 5: The phase diagram for $N=2$ and $P= -0.009987500000000$; $\epsilon=10$ for $0 \leq x \leq 30$, $x_{2} \leq x \leq 100$ and $\epsilon=5$ for $x_{1}<x<x_{2}$. Dotted, dash-dotted, dashed and solid curves $x_{2}$ are corresponded to $35, 40, 45$ and $50$ respectively.