Relativistic k-fields with massless soliton solutions in $$3+1$$ dimensions

In this work, the relativistic non-standard Lagrangian densities (k-fields) with massless solutions are generally introduced. Such not necessarily energetically stable. However, in $$3+1$$ dimensions, we introduce a new k-field model that results single non-topological solitary wave solution. This special solution is stable; is, any arbitrary deformation above its background leads to an increase total energy. other words, energy zero which least all solutions. Hence, it can be called soliton