<p>The primary aim of this article is to derive variational principles and analytical solutions for nonlinear partial differential Riemann wave equations and the Landau-Ginsburg-Higgs equation, both of which have recently attracted interest in various physical fields. To achieve this, we employ the direct integration along with the semi-inverse method. Our findings indicate that the semi-inverse method effectively yields variational formulations and analytical solutions for these nonlinear partial differential equations. The semi-inverse method’s succinct formulation and ease of deriving variational formulations render it significant for its applicability to an extensive variety of nonlinear partial differential equations.</p>