Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

Abstract

In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of $N$ slow kinks in the sine-Gordon model were calculated analytically (for $N=1,2$, and 3) and numerically (for $4\le N\le 7$). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the two components of the potential energy density and (ii) the extreme values of elastic strain. Our results suggest that in multi-soliton collisions the main contribution to the potential energy density comes from the elastic strain, but not from the on-site potential. It is also found that tensile strain is usually larger than compressive strain in the core of multi-soliton collision.

arXiv comment9 pages, 6 figures. arXiv admin note: text overlap with arXiv:1605.09767

References in corpus (18)

• Nonlinear switching and solitons in PT-symmetric photonic systems
• Kink-antikink collisions in the phi^6 model
• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
• Kink excitation spectra in the (1+1)-dimensional ${\phi }^8$ model
• Two-soliton collisions in a near-integrable lattice system
• Successive phase transitions and kink solutions in ${\varphi }^8$, ${\varphi }^{10}$, and ${\varphi }^{12}$ field theories
• Multi-kink collisions in the ${\varphi }^6$ model
• Resonances in the dynamics of ${\varphi }^4$ kinks perturbed by ac forces
• Discrete Klein-Gordon models with static kinks free of the Peierls-Nabarro potential
• Kinks and antikinks of buckled graphene: A testing ground for phi^4 field model
• High energy density in the collision of $N$ kinks in the ${\varphi }^4$ model
• Interaction of topological solitons with defects: using a nontrivial metric
• Analytical formulation for soliton-potential dynamics
• Motion of domain walls and the dynamics of kinks in the magnetic Peierls potential
• High energy density in multi-soliton collisions
• Radiationless energy exchange in three-soliton collisions
• Search for long-living topological solutions of nonlinear ${\phi }^4$ field theory

Cited by in corpus (29)

• Scattering of the double sine-Gordon kinks
• Kink-Antikink Collisions and Multi-Bounce Resonance Windows in Higher-Order Field Theories
• Multi-kink scattering in the double sine-Gordon model
• Interaction between kinks and antikinks with double long-range tails
• Non-topological kink scattering in a two-component scalar field theory model
• Explicit kinks in higher-order field theories
• Kink scattering in a hybrid model
• Collision of two kinks with inner structure
• Oscillons in hyperbolic models
• Wobbling double sine-Gordon kinks
• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Kink-antikink collisions in the ${\varphi }^8$ model: short-range to long-range journey
• Kink scattering in hyperbolic models
• Kink-antikink collision in a Lorentz-violating ${\varphi }^4$ model
• False vacuum decay in kink scattering
• Asymmetric kink scattering in a two-component scalar field theory model
• Quasinormal modes in kink excitations and kink-antikink interactions: a toy model
• Collision of ${\varphi }^4$ kinks free of the Peierls-Nabarro barrier in the regime of strong discreteness
• A new look at the double sine-Gordon kink-antikink scattering
• Semi-compactness and multiple oscillating pulses in kink scattering
• Kink scattering in the presence of geometric constrictions
• Kink-antikink scattering-induced breathing bound states and oscillons in a parametrized ${\varphi }^4$ model
• Differential configurational entropy for multi-field of the ${\varphi }^6$ theory
• Geometrically constrained sine-Gordon field: BPS solitons and their collisions
• Kinks in the relativistic model with logarithmic nonlinearity
• Scattering of kinks in scalar-field models with higher-order self-interactions
• Kink dynamics in a high-order field model
• Kink scattering in a Lorentz-violating ${\varphi }^6$ model
• Kinks scattering in deformed ${\phi }^6$ model