  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.
