Similarity transformations and exact solutions of the generalized (<inline-formula><tex-math id="M3">\begin{document}$ n+1 $\end{document}</tex-math></inline-formula>)-dimensional Schrödinger equation with (<inline-formula&

Schrödinger-type equations represent a fundamentally important class of differential equations. Research on high-dimensional variable-coefficient Schrödinger-type equations as important theoretical and practical value, providing critical insights into the dynamics of complex wave phenomena. In this paper, we employ similarity transformations to derive a novel class of soliton solutions for the (<i>n</i> + 1)-dimensional (2<i>m</i> + 1)th-order variable-coefficient nonlinear Schrödinger equation. By extending similarity transformations from lower-dimensional to higher dimensionnal equations, we establish the intrinsic relationships among the equation’s coefficients. Furthermore, utilizing the solutions of the stationary Schrödinger equation and using the balancing-coefficient method, we construct both bright and dark soliton solutions for the (<i>n</i> + 1)-dimensional (2<i>m</i> + 1)th-order variable-coefficient nonlinear Schrödinger equation. Finally, for specific cases, we present graphical representations of the bright and dark soliton solutions and conduct a systematic analysis of their spatial structures and propagation characteristics. Our results indicate that bright solitons exhibit a single-peak structure, while dark solitons form trough-like profiles, further confirming the stability of soliton wave propagation.