  In the construction of a classical smoothed out brane world model in five
dimensions, one uses a dynamically generated domain wall (a kink) to localise
an effective four dimensional theory. At the level of the Euler-Lagrange
equations the kink sets up a potential well, a mechanism which has been
employed extensively to obtain localised, four dimensional, massless chiral
fermions. We present the generalisation of this kink trapping mechanism for
both scalar and fermionic fields, and retain all degrees of freedom that were
present in the higher dimensional theory. We show that a kink background
induces a symmetric modified Poschl-Teller potential well, and give explicit
analytic forms for all the bound modes and a restricted set of the continuum
modes. We demonstrate that it is possible to confine an effective four
dimensional scalar field with a quartic potential of arbitrary shape. This can
be used to place the standard model electroweak Higgs field on the brane, and
also generate nested kink solutions. We also consider the limits of the
parameters in the theory which give thin kinks and localised and de-localised
scalar and fermionic fields.
