Domain wall thickness and deformations of the field model

Blinov, Petr A.; Gani, Tatiana V.; Gani, Vakhid A.

doi:10.1088/1742-6596/1690/1/012085

Cited by 6 publications

(5 citation statements)

References 27 publications

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“…The discrete spectrum in the potential well U (x) contains only zero mode, the corresponding eigenfunction is asymmetric and can be found from Eqs. ( 14) and (27).…”

Section: Kinks In a Class Of Polynomial Modelsmentioning

confidence: 99%

“…5. The transformation properties of the kink asymptotics with respect to the deformation procedure have been studied [26,27]. A class of deformation functions has been found that transform the power-law asymptotics into power-law, but it was shown that the speed of the field approaching the vacuum value (the power of the coordinate in the asymptotic expression for the field) can change.…”

Section: Introductionmentioning

confidence: 99%

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Kinks in higher-order polynomial models

Blinov¹,

Gani²,

Malnev³

et al. 2022

Chaos, Solitons & Fractals

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“…The discrete spectrum in the potential well U (x) contains only zero mode, the corresponding eigenfunction is asymmetric and can be found from Eqs. ( 14) and (27).…”

Section: Kinks In a Class Of Polynomial Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kinks in higher-order polynomial models

Blinov¹,

Gani²,

Malnev³

et al. 2022

Chaos, Solitons & Fractals

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“…Several years ago Bazeia et al [66] proposed a novel deformation function f (φ) = 1 − φ 2 and discussed some of its properties. Subsequently, a lot of work has been done about various other deformation functions [10,67,68,69,70,71]. Recently we [72] have generalized the deformation function of [66] and proposed a one-parameter family of deformation functions f (φ) = (1−φ 2n ) 1/2n , n = 1, 2, 3, ... having novel and very unusual properties such as being its own inverse and starting from certain potentials such a deformation can either create or destroy an arbitrary even number of kink solutions.…”

Section: Kink-antikink Collisions At Finite Velocitymentioning

confidence: 99%

Kink Solutions With Power Law Tails

Khare¹,

Saxena²

2022

Preprint

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Table of Contents 1. Introduction 2. Kink formalism 3. Kinks with power law tails of the form eppe4. Kinks with power law tails of the form peep 5. Kinks with power law tails of the form pppp 6. Kinks with power-tower tails 7. Kinks with kink tails of the form eeep 8. Kinks with kink tails of the form pppe 9. Explicit kink solutions with power law tails 10. Kink-kink and kink-antikink forces for power law tails 11. Kink-antikink collisions at finite velocity 12. Open problems

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“…13) Several years ago Bazeia et al [66] proposed a novel deformation function f(ϕ) 1 − ϕ 2 and discussed some of its properties. Subsequently, a lot of work has been done about various other deformation functions [10,[67][68][69][70][71].…”

Section: Open Problemsmentioning

confidence: 99%

Kink solutions with power law tails

Khare

Saxena

2022

Front. Phys.

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We present a comprehensive review about the various facets of kink solutions with a power law tail, which have received considerable attention during the last few years. This area of research is in its early stages; although several aspects have become clear by now, there are a number of issues which have only been partially understood or not understood at all. We first discuss the aspects which are reasonably well known and then address in some detail the issues which are only partially or not understood at all. We present a wide class of higher (than sixth) order field theory models admitting implicit kink as well as mirror kink solutions where the two tails facing each other have a power law or a power-tower type fall off, whereas the other two ends not facing each other could have either an exponential or a power law tail. The models admitting implicit kink solutions where the two ends facing each other have an exponential tail while the other two ends have a power law tail are also discussed. Moreover, we present several field theory models which admit explicit kink solutions with a power law fall off; we note that in all these polynomial models while the potential V(ϕ) is continuous, its derivative is discontinuous. We also discuss one of the most important and only partially understood issues of the kink–kink and the kink–antikink forces in case the tails facing each other have a power law fall off. Finally, we briefly discuss the kink–antikink collisions at finite velocity and present some open questions.

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Domain wall thickness and deformations of the field model

Cited by 6 publications

References 27 publications

Kinks in higher-order polynomial models

Kinks in higher-order polynomial models

Kink Solutions With Power Law Tails

Kink solutions with power law tails

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