Kink interactions in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>φ</mml:mi><mml:mn>6</mml:mn></mml:msup></mml:math>model

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

doi:10.1103/physrevd.89.125009

Cited by 129 publications

(163 citation statements)

References 33 publications

Supporting

Mentioning

156

Contrasting

Order By: Relevance

“…We use the same values of x 1 , x 2 , v 1 , and v 2 as in the previous subsection. The critical velocity value in this case is smaller than in the previous configuration, namely, v cr ≈ 0.045 [26,27]. The initial velocity of the kinks in our numerical experiment is more than the critical value.…”

Section: The Configuration (101)mentioning

confidence: 70%

“…The (1+1)-dimensional φ 6 model is well-known in the literature [26,27,41,42,52], but the study of simultaneous multi-kink collisions in this model is carried out for the first time. A simultaneous collision of several kinks in a small region can produce a very large energy density in this region.…”

Section: Jhep07(2017)028mentioning

confidence: 99%

“…The interactions of kinks (and antikinks) are studied using different methods, in particular, quasi-exact methods such as the numerical solution of the equations of motion, which are partial differential equations, and approximate methods such as the collective coordinate approximation [27,[41][42][43][44][45][46] and the Manton's method [47][48][49]. The simple collective…”

Section: Introductionmentioning

confidence: 99%

“…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%

See 3 more Smart Citations

Multi-kink collisions in the ϕ 6 model

Marjaneh

Gani

Saadatmand

et al. 2017

J. High Energ. Phys.

Self Cite

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

Section: The Configuration (101)mentioning

confidence: 70%

Section: Jhep07(2017)028mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-kink collisions in the ϕ 6 model

Marjaneh

Gani

Saadatmand

et al. 2017

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The tail asymptotics that we derived for the kinks above could be used, in conjunction with Manton's approach [35], to compute (asymptotically, for large separations) kink-kink and kink-anti-kink interaction energies [36]. It would also be of interest to determine whether the implicit kink solutions can be used to study interactions via the collective-coordinate variational approximation techniques previously applied to the φ 4 [37,38], φ 6 [39] and sine-Gordon [40,41] field theories.…”

Section: Discussionmentioning

confidence: 99%

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

View full text Add to dashboard Cite

We obtain exact solutions for kinks in φ 8 , φ 10 and φ 12 field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponentialalgebraic tail decay, unlike the lower-order φ 4 and φ 6 theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a φ 12 potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the φ 10 field theory, which is a quasi-exactly solvable (QES) model akin to φ 6 , we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.

show abstract

$$\phi ^4$$ Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics

Ross

Kevrekidis

Campbell

et al. 2019

Nonlinear Systems and Complexity

View full text Add to dashboard Cite

We explore a φ 4 model with an added external parabolic potential term. This term dramatically alters the spectral properties of the system. We identify single and multiple kink solutions and examine their stability features; importantly, all of the stationary structures turn out to be unstable. We complement these with a dynamical study of the evolution of a single kink in the trap, as well as of the scattering of kink and anti-kink solutions of the model. We see that some of the key characteristics of kink-antikink collisions, such as the critical velocity and the multi-bounce windows, are sensitively dependent on the trap strength parameter, as well as the initial displacement of the kink and antikink.The Euler-Lagrange equations in this case with respect to X and A give

show abstract

Kink interactions in the(1+1)-dimensionalφ6model

Cited by 129 publications

References 33 publications

Multi-kink collisions in the ϕ 6 model

Multi-kink collisions in the ϕ 6 model

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

$$\phi ^4$$ Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics

Contact Info

Product

Resources

About