Perturbations of the signum-Gordon model

Klimas, P.

doi:10.1088/1751-8113/41/9/095403

Cited by 5 publications

(10 citation statements)

References 9 publications

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“…As it was pointed out in [49], the perturbative method applied to a self-similar initial data leads to an exact solution. However, it also requires some extremely lengthy computations.…”

Section: Solution Formentioning

confidence: 90%

“…To make any progress with this problem we make an approximation which is similar in nature to what was made in [49]. This approximation led to the study of the evolution of some self-similar initial data in a model with a broken scaling symmetry [49]. We have to stress, however, that, in general, it is not possible to construct any analytical solution which is valid for all times.…”

Section: Approximate Oscillon Solutionsmentioning

confidence: 99%

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Oscillons in a perturbed signum-Gordon model

Klimas

Streibel

Wereszczyński

et al. 2018

J. High Energ. Phys.

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Abstract:We study various properties of a perturbed signum-Gordon model, which has been obtained through the dimensional reduction of the called 'first BPS submodel of the Skyrme model'. This study is motivated by the observation that the first BPS submodel of the Skyrme model may be partially responsible for the good qualities of the rational map ansatz approximation to the solutions of the Skyrme model. We investigate the existence, stability and various properties of oscillons and other time-dependent states in this perturbed signum-Gordon model.

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“…As it was pointed out in [49], the perturbative method applied to a self-similar initial data leads to an exact solution. However, it also requires some extremely lengthy computations.…”

Section: Solution Formentioning

confidence: 90%

Section: Approximate Oscillon Solutionsmentioning

confidence: 99%

Oscillons in a perturbed signum-Gordon model

Klimas

Streibel

Wereszczyński

et al. 2018

J. High Energ. Phys.

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“…In order to develop some geometric understanding of these new coupled BPS submodels and their Bogomolny equations, we use the well know formulation of the static energy integral of the L 24 Skyrme model in terms of the eigenvalues λ 2 i of the strain tensor [13], [14],…”

Section: Geometric Meaningmentioning

confidence: 99%

“…This can be resolved by also "squeezing" the configuration from the inner region which is achieved by the following boundary conditions ξ(r = R 1 ) = π and ξ(r = R 2 ) = 0 (IV. 24) or equivalently, ξ(y = R −1 2 ) = 0 and ξ(y = R −1 1 ) = π.…”

Section: Bps Model and Non-zero Pressurementioning

confidence: 99%

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BPS sectors of the Skyrme model and their non-BPS extensions

et al. 2018

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Two recently found coupled BPS submodels of the Skyrme model are further analyzed. Firstly, we provide a geometrical formulation of the submodels in terms of the eigenvalues of the strain tensor. Secondly, we study their thermodynamical properties and show that the mean-field equations of state coincide at high pressure and read p =ρ/3. We also provide evidence that matter described by the first BPS submodel has some similarity with a Bose-Einstein condensate. Moreover, we show that extending the second submodel to a non-BPS model by including certain additional terms of the full Skyrme model does not spoil the respective ansatz, leading to an ordinary differential equation for the profile of the Skymion, for any value of the topological charge. This allows for an almost analytical description of the properties of Skyrmions in this model. In particular, we analytically study the breaking and restoration of the BPS property. Finally, we provide an explanation of the success of the rational map ansatz.

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Compact shell solitons in K field theories

Adam¹,

Klimas²,

Sánchez-Guillén³

et al. 2009

Journal of Mathematical Physics

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Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological solitons, and may be classified as maps $S^3 \to S^3$ and suspended Hopf maps, respectively. The Lagrangian of these models is given by a scalar field with a non-standard kinetic term (K field) coupled to a pure Skyrme term restricted to $S^2$, rised to the appropriate power to avoid the Derrick scaling argument. Further, the existence of infinitely many exact shell solitons is explained using the generalized integrability approach. Finally, similar models allowing for non-topological compactons of the ball type in 3+1 dimensions are briefly discussed.Comment: 10 pages, latex, 2 figures, change in title and introduction. Discussion section, 2 figures and references adde

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Perturbations of the signum-Gordon model

Cited by 5 publications

References 9 publications

Oscillons in a perturbed signum-Gordon model

Oscillons in a perturbed signum-Gordon model

BPS sectors of the Skyrme model and their non-BPS extensions

Compact shell solitons in K field theories

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