Meromorphic Solutions for a Class of Two-Dimensional Quasilinear Hyperbolic Conservation Laws

Quasilinear hyperbolic conservation law equations are of great significance in mathematical physics. Characterizing their meromorphic solutions provides valuable insight into the qualitative behaviors of these equations. In this paper, we investigate a two-dimensional quasilinear hyperbolic conservation law equation. By virtue of Nevanlinna theory and rigorous analytic arguments, we derive the explicit forms of its meromorphic solutions. Furthermore, under suitable initial conditions, we analyze the dynamical properties of the obtained soliton-type solutions.