The present work investigates several models of a single real scalar field, engendering kinetic term of the Dirac-Born-Infeld type. Such theories introduce nonlinearities to the kinetic part of the Lagrangian, which presents a square root restricting the field evolution and including additional powers in derivatives of the scalar field, controlled by a real parameter. In order to obtain topological solutions analytically, we propose a first-order framework that simplifies the equation of motion ensuring solutions that are linearly stable. This is implemented using the deformation method, and we introduce examples presenting two categories of potentials, one having polynomial interactions and the other with nonpolynomial interactions. We also explore how the Dirac-Born-Infeld kinetic term affects the properties of the solutions. In particular, we note that the kinklike solutions are similar to the ones obtained through models with standard kinetic term and canonical potential, but their energy densities and stability potentials vary according to the parameter introduced to control the new models.

In this work we investigate the transition from kinks to compactons at high temperatures. We deal with a family of models, described by a real scalar field with standard kinematics, controlled by a single parameter, real and positive. The family of models supports kink-like solutions, and the solutions tend to become compact when the parameter increases to larger and larger values. We study the oneloop corrections at finite temperature, to see how the thermal effects add to the effective potential. The results suggest that the symmetry is restored at very high temperatures.

This work reports on models described by two real scalar fields coupled with gravity in the five-dimensional spacetime, with a warped geometry involving one infinite extra dimension. Through a mechanism that smoothly changes a thick brane into a hybrid brane, one investigates the appearance of hybrid branes hosting internal structure, characterized by the splitting on the energy density and the volcano potential, induced by the parameter which controls interactions between the two scalar fields. In particular, we investigate distinct symmetric and asymmetric hybrid brane scenarios.

In this work we investigate several models described by a single real scalar field with non-polynomial interactions, constructed to support topological solutions. We do this using the deformation procedure to introduce a function which allows to construct two distinct families of hyperbolic potentials, controlled by three distinct parameters, in the standard formalism. In this way, the procedure allows us to get analytical solutions, and then investigate the energy density, linear stability and zero mode. We move on and introduce a non-standard formalism to obtain compact solutions, analytically. We also investigate these hyperbolic models in the braneworld context, considering both the standard and non-standard possibilities. The results show how to construct distinct braneworld models which are implemented via the first order formalism and are stable against fluctuation of the metric tensor.Comment: 20 pages, 13 figures; version to appear in IJMP

-We demonstrate that the complete factorization of equations of motion into first-order differential equations can be obtained for real and complex scalar field theories with non-canonical dynamics.Introduction. -In 1934, Born and Infeld (BI) proposed a nonlinear generalization of electrodynamics [1] to avoid the divergence problem with the electron self-energy. It is an important example where nonlinear dynamics may play a role and it was later shown that such action, now called DBI action [1,2], arises naturally in the context of string theory [3]. Some examples of its usage can be seen as, for instance: an effective action for the tachyon condensation [4]; a string theory model to describe the early inflationary period of the universe [5]; in cosmology a scalar DBI action can be used to describe the acceleration of the universe [6], as well as the inflationary period in the early universe [7]; models with the presence of instanton solutions [8], the description of global strings [9]; vortex solutions [10,11]; formulation of twinlike models [12] and so on. More recently, several analytical models described within the DBI context admitting kinks solutions were explored in Ref. [13]. The DBI model opened up a new road to consider non-canonical dynamics and to deal with more general forms of the kinetic term.Domain walls and branes have drawn a lot of attention to the physics community [14] and may appear when the scalar field has nonlinear dynamics as well. Some examples include: in [15] one investigates specific features of kinks and vortices; in [16][17][18][19] one studies how the modifications on the kinetic part of the Lagrangian introduce new nonlinear terms to the equations of motion, which can permit the appearance of compact solutions [16][17][18], also known as compactons [20]; in [21] the defect structure within a scalar generalized profile is studied; and in [22,23] the braneworld scenario is also investigated.