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We study how the properties of a Lagrangian density for a single real scalarfield in flat spacetime change with inclusion of an overall factor dependingonly on the field. The focus of the paper is to obtain analytical results. So,we show that even though it is possible to perform a field redefinition to getan equivalent canonical model, it is not always feasible to write the canonicalmodel in terms of elementary functions. Also, we investigate the behavior ofthe energy density and the linear stability of the solutions. Finally, we showthat one can find a class of models that present the same energy density andthe same stability potential.

Generalized scalar field models with the same energy density and linear stability