<p>Recent studies have extensively explored fixed hopping in zig–zag lattices. However, material heating effects can induce inhomogeneity, significantly altering the lattice’s shape and behavior. Motivated by this, we introduce a novel approach by constructing both discrete and continuum models for a zig–zag lattice with space-dependent hopping between two-nearest-neighbor interactions. The primary objective of this study is to investigate the impact of inhomogeneity on photon transport characteristics. To achieve this, we derive exact solutions for the inhomogeneous continuum model using the extended unified method. Our findings reveal key insights, including a significant enhancement in photon transport within lattices featuring variable hopping. Furthermore, we explore the influence of this property on nonlinear optical wave structures, uncovering various topological solitons such as clustered zig–zag solitons near the origin, dark solitons, and spiky tree-like structures with leaf-like features. Additionally, we examine modulated wave-amplitude gain, providing a deeper understanding of and control over nonlinear optical wave behavior.</p>