Compacton formation under Allen–Cahn dynamics

Cirillo, Emilio N. M.; Ianiro, Nicoletta; Sciarra, Giulio

doi:10.1098/rspa.2015.0852

Cited by 6 publications

(3 citation statements)

References 21 publications

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“…By substituting this expression in the equation (13) we have that the linearized equation can be written as…”

Section: Linear Stabilitymentioning

confidence: 99%

“…The fact that ε is strictly positive will be crucial in this paper, indeed, it has been proven in different contexts, see, e.g., [13,14,15], that if the stiffness is allowed to vanish in correspondence of the homogeneous states, not regular stationary solutions, often called compactons [16], can be found.…”

Section: Introductionmentioning

confidence: 97%

“…In this paper we consider the case in which the higher-order stiffness is not constant [11,12,13], but it is a sufficiently regular positive function of the field, namely, ε ∈ C ∞ (R) such that there is C > 1 for which…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability of the stationary solutions of the Allen-Cahn equation with non-constant stiffness

Buttà¹,

Cirillo²,

Sciarra³

2020

Preprint

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“…By substituting this expression in the equation (13) we have that the linearized equation can be written as…”

Section: Linear Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Stability of the stationary solutions of the Allen-Cahn equation with non-constant stiffness

Buttà¹,

Cirillo²,

Sciarra³

2020

Preprint

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show abstract

Exponentially slow motion of interface layers for the one-dimensional Allen–Cahn equation with nonlinear phase-dependent diffusivity

Folino

Melo

Ríos

et al. 2020

Z. Angew. Math. Phys.

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Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules

Sergyeyev

Skurativskyi

Vladimirov

2019

Nonlinear Analysis: Real World Applications

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We present the results of study of a nonlinear evolutionary PDE (more precisely, a oneparameter family of PDEs) associated with the chain of pre-stressed granules. The PDE in question supports solitary waves of compression and rarefaction (bright and dark compactons) and can be written in Hamiltonian form. We investigate inter alia integrability properties of this PDE and its generalized symmetries and conservation laws.For the compacton solutions we perform a stability test followed by the numerical study. In particular, we simulate the temporal evolution of a single compacton, and the interactions of compacton pairs. The results of numerical simulations performed for our model are compared with the numerical evolution of corresponding Cauchy data for the discrete model of chain of pre-stressed elastic granules.

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Compacton formation under Allen–Cahn dynamics

Abstract: International audienc

Cited by 6 publications

References 21 publications

Stability of the stationary solutions of the Allen-Cahn equation with non-constant stiffness

Stability of the stationary solutions of the Allen-Cahn equation with non-constant stiffness

Exponentially slow motion of interface layers for the one-dimensional Allen–Cahn equation with nonlinear phase-dependent diffusivity

Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules

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