Nonlinear wave equations and first order complex quasilinear equations

In this paper, we establish a connection between the complex quasi-linear first-order equations and multidimensional nonlinear hyperbolic and elliptic equations that describe wave propagation phenomena of various types in nonlinear media in multidimensional spaces. Multivalued exact solutions are constructed. Spatial structure and dynamics of multivalued exact solutions along the complex characteristics are analyzed. The boundaries of the uniqueness of solutions are explored.