Effect of the ϕ4 kink’s internal mode at scattering on a PT-symmetric defect

Saadatmand, Danial; Борисов, Д. И.; Kevrekidis, P. G.; Fatykhov, M. A.; Javidan, Kurosh

doi:10.1134/s0021364015070140

Cited by 20 publications

(25 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The simplest nonintegrable and largely studied is the λφ 4 model [14][15][16][17][18][19][20][21][22][23]. In that model, for larger initial velocities v we have inelastic scattering, with the pair of solitons colliding once and separating thereafter.…”

Section: Introductionmentioning

confidence: 99%

Kink scattering in a hybrid model

et al. 2019

View full text Add to dashboard Cite

In this work we consider a model where the potential has two topological sectors connecting three adjacent minima, as occurs with the φ 6 model. In each topological sector, the potential is symmetric around the local maximum. For φ > 0 there is a linear map between the model and the λφ 4 model. For φ < 0 the potential is reflected. Linear stability analysis of kink and antikink lead to discrete and continuum modes related by a linear coordinate transformation to those known analytically for the λφ 4 model. Fixing one topological sector, the structure of antikinkkink scattering is related to the observed in the λφ 4 model. For kink-antikink collisions a new structure of bounce windows appear. Depending on the initial velocity, one can have oscillations of the scalar field at the center of mass even for one bounce, or a change of topological sector. We also found a structure of one-bounce, with secondary windows corresponding to the changing of the topological sector accumulating close to each one-bounce windows. The kink-kink collisions are characterized by a repulsive interaction and there is no possibility of forming a bound state.

show abstract

Section: Introductionmentioning

confidence: 99%

Kink scattering in a hybrid model

et al. 2019

View full text Add to dashboard Cite

show abstract

“…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.

View full text Add to dashboard Cite

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.

show abstract

“…We seek the solution to problem (25) with f = f ⊥ in the space L ⊥ ∩ W 2 2 (R 2 ). It is easy to check that space V is an invariant one for operator H. Given arbitrary ψ ∈ L ⊥ ∩ W 2 2 (R 2 ), we employ the definition of 0 and space L ⊥ and proceed as in (24):…”

Section: Proof Of Main Resultsmentioning

confidence: 99%

“…Kevrekidis has developed a collective variable method to describe the dynamics of kinks in 1D Klein-Gordon field in the presence of PT -symmetric perturbation [23]. In the later works, this method was applied to the sine-Gordon [24] and φ 4 [25,26] models. In the latter case, the effect of the kink's internal mode on the interaction of the kink with PT -symmetric impurity was analyzed.…”

Section: Introductionmentioning

confidence: 99%

On the Spectral Stability of Kinks in 2D Klein–Gordon Model with Parity‐Time‐Symmetric Perturbation

Борисов

2016

Stud Appl Math

Self Cite

View full text Add to dashboard Cite

In a series of recent works by Demirkaya et al. stability analysis for the static kink solutions to the 1D continuous and discrete Klein-Gordon equations with a PT -symmetric perturbation has been analysed. We consider the linear stability problem for the static kink in 2D Klein-Gordon field taking into account spatially localized PT -symmetric perturbation. The perturbation is in the form of viscous friction, which does not affect the static solutions to the unperturbed Klein-Gordon equation. Small dynamic perturbation around the static kink solution is considered to formulate the linear stability problem. The effect of the small perturbation on the solutions to the corresponding eigenvalue problem is analysed. The main result is presented in the form of a theorem describing the behavior of the eigenvalues corresponding to the extended and localised eigenmodes as the functions of the perturbation parameter.

show abstract

Effect of the ϕ4 kink’s internal mode at scattering on a PT-symmetric defect

Cited by 20 publications

References 23 publications

Kink scattering in a hybrid model

Kink scattering in a hybrid model

Multi-kink collisions in the ϕ 6 model

On the Spectral Stability of Kinks in 2D Klein–Gordon Model with Parity‐Time‐Symmetric Perturbation

Contact Info

Product

Resources

About