Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies

Gani, Vakhid A.; Kudryavtsev, A. E.

doi:10.1103/physreve.60.3305

Cited by 113 publications

(113 citation statements)

References 6 publications

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“…[28] (where a very comprehensive study of escape windows in the ϕ 6 model was given). A similar mechanism is involved in the so-called quasiresonances in the double sine-Gordon model [37].…”

Section: Kink Collisions In the ϕ 6 Modelmentioning

confidence: 88%

Kink interactions in the(1+1)-dimensionalφ6model

2014

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We study kink scattering processes in the (1+1)-dimensional ϕ 6 model in the framework of the collective coordinate approximation. We find critical values of the initial velocities of the colliding kinks. These critical velocities distinguish different regimes of collisions. The exact equation of motion for the ϕ 6 model is also solved numerically with the same initial conditions.We discuss advantages and disadvantages of the collective coordinate approximation, and also outline its applicability limits. Resonance phenomena and the so-called escape windows are also observed in the kink collisions.

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Section: Kink Collisions In the ϕ 6 Modelmentioning

confidence: 88%

Kink interactions in the(1+1)-dimensionalφ6model

2014

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“…Multi-soliton solutions to the sine-Gordon (sG) equation have been derived analytically [20,21] and analyzed by many authors [22,23,24,25,26,27,28,29,30,31]. Colliding solitons can produce high energy density spots and for many applications it is important to know how large the energy density can be in multi-soliton collisions.…”

Section: Introductionmentioning

confidence: 99%

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

2018

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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 ≤ N ≤ 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 multisoliton 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.PACS. 05.45.Yv Solitons -11.10.Lm Nonlinear or nonlocal theories and models -45.50.Tn Collisions

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“…In particular, the kink-(anti)kink scattering and the interactions of kinks with impurities are of growing interest. A wide variety of phenomena emerges in these systems, e.g., escape windows and quasi-resonances in kink-(antikink) collisions [20][21][22][23][24][25][26][27][28][29][30], resonant interactions of kinks with wells, barriers and impurities [31][32][33][34], non-radiative energy exchange in multi-soliton collisions [35][36][37]. It is interesting that the presence of a kink's internal modes does not guarantee the appearance of resonance windows, as it has been recently shown for the deformed φ 4 model [38].…”

Section: Introductionmentioning

confidence: 99%

Multi-kink collisions in the ϕ 6 model

Marjaneh

Gani

Saadatmand

et al. 2017

J. High Energ. Phys.

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We study simultaneous collisions of two, three, and four kinks and antikinks of the φ 6 model at the same spatial point. Unlike the φ 4 kinks, the φ 6 kinks are asymmetric and this enriches the variety of the collision scenarios. In our numerical simulations we observe both reflection and bound state formation depending on the number of kinks and on their spatial ordering in the initial configuration. We also analyze the extreme values of the energy densities and the field gradient observed during the collisions. Our results suggest that very high energy densities can be produced in multi-kink collisions in a controllable manner. Appearance of high energy density spots in multi-kink collisions can be important in various physical applications of the Klein-Gordon model.

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Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies

Cited by 113 publications

References 6 publications

Kink interactions in the(1+1)-dimensionalφ6model

Kink interactions in the(1+1)-dimensionalφ6model

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

Multi-kink collisions in the ϕ 6 model

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