  We study a scalar field model in a two dimensional space-time with a
generalized $\phi^4_G$ potential which has four minima, obtaining novel kink
solutions with well defined properties although the potential is non-analytical
at the origin. The model contains a control parameter $\delta$ that breaks the
degeneracy of the potential minima, giving rise to two different phases for the
system. The $\delta<0$ phases do not possess solitary wave solutions. At the
transition point $\delta=0$ all the potential minima are degenerate and three
different kink solutions result. As the transition to the $\delta>0$ phase
takes place, the minima of the potential are no longer degenerate and a unique
kink $\phi_\delta$ solution is produced. Remarkably, this kink is a coherent
structure that results from the merge of three kinks that can be identified
with those observed at the transition point. To support the interpretation of
$\phi_\delta$ as a bound state of three kinks, we calculate the force between
the kink-kink pair components of $\phi_\delta$, obtaining an expression that
has both exponentially repulsive and constant attractive contributions that
yields an equilibrium configuration, explaining the formation of the
$\phi_\delta$ multi-kink state. We further investigate kink properties
including their stability guaranteed by the positive defined spectrum of small
fluctuations around the kink configurations. The findings of our work together
with a semiclassical WKB quantization, including the one loop mass
renormalization, enable computing quantum corrections to the kink masses. The
general results could be relevant to the development of effective theories for
non-equilibrium steady states and for the understanding of the formation of
coherent structures.
