Related papers: Stable static structures in models with higher-ord…

Discrete symmetries are commonplace in field theoretical models but pose a severe problem for cosmology since they lead to the formation of domain walls during spontaneous symmetry breaking in the early universe. However if one of the…

Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…

Derrick's theorem on the nonexistence of stable time-independent scalar field configurations [G. H. Derrick, J. Math. Phys. 5, 1252 (1964)] is generalized to finite systems of arbitrary dimension. It is shown that the "dilation" argument…

In this manuscript using the asymptotic method of multiscale nonlinear theory we construct a nonlinear theory of the appearance of large-scale structures in the stratified conductive medium with the presence of small-scale oscillations of…

The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…

The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at…

We study a model with a real scalar Higgs field and a scalar triplet field that allows existence of a topological defect -- a domain wall. The wall breaks the global $O(3)$ symmetry of the model, which gives rise to non-Abelian…

We study the stability of topological structures in generalized models with a single real scalar field. We show that it is driven by a Sturm-Liouville equation and investigate the conditions that lead to the existence of explicit…

We investigate several models described by real scalar fields, searching for topological defects, and investigating their linear stability. We also find bosonic zero modes and examine the thermal corrections at the one-loop level. The…

We introduce domain-wall (DW) states in the bimodal discrete nonlinear Schr{\"{o}}dinger equation, in which the modes are coupled by cross phase modulation (XPM). By means of continuation from various initial patterns taken in the…

We consider the Kawahara model and two fourth order semi-linear Schr\"odinger equations in any spatial dimension. We construct the corresponding normalized ground states, which we rigorously show to be spectrally stable. For the Kawahara…

We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…

We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the…

We show that the spacetimes of domain wall solutions to the coupled Einstein-scalar field equations with a given scalar field potential fall into two classes, depending on whether or not reflection symmetry on the wall is imposed. Solutions…

We study the dynamics of domain walls in a double-field model in which the U(1) symmetry is broken both spontaneously and explicitly. The global U(1) symmetry of the system is restored when the symmetry breaking parameter $\epsilon$ is set…

This study offers a detailed analysis of domain wall formation and its cosmological consequences in Einstein-Gauss-Bonnet gravity coupled to a scalar field. A central aspect of the model is the scalar field Lagrangian's ability to…

We perform a linear stability analysis of extended domains in phase-separating fluids of equal viscosity, in two dimensions. Using the coupled Cahn-Hilliard and Stokes equations, we derive analytically the stability eigenvalues for long…

One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…

We construct cosmological models with two scalar fields, which has the structure as in the ghost condensation model or k-essence model. The models can describe the stable phantom crossing, which should be contrasted with one scalar tensor…

Mackey-Glass equation arises in the leukemia model. We generalize this equation to include fractional-order derivatives in two directions. The first generalization contains one whereas the second contains two fractional derivatives. Such…