<p>This paper studies the well–posedness and averaging for the dispersion–managed nonlinear Schrödinger equation (NLS) with general nonlinearity, where the dispersion map <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> <EquationSource Format="TEX">$\gamma $</EquationSource> </InlineEquation> is assumed to be piecewise constant. We establish the local well–posedness of the equation in the Sobolev space <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mi>m</mi> </msup> <mo stretchy="false">(</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>N</mi> </msup> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$H^{m}(\mathbb{R}^{N})$</EquationSource> </InlineEquation> by applying a fixed–point theorem. Furthermore, we analyze the convergence of the solutions of the original equation to the solutions of the averaged equation. The analysis relies on linear propagators and Strichartz estimates to derive the main results. This study helps us improve our understanding of the dynamic behavior of dispersion–managed NLS and provides a mathematical framework that can be used in different physical systems.</p>