Demonstrates multidimensional exact solutions of a hyperbolic equation, suggesting new mathematical approaches.
A reduction method using additive, multiplicative, and functional separation of variables is applied to a hyperbolic equation with the Monge–Ampère operator. We obtain multidimensional exact solutions expressed in closed form via elementary and special functions and/or solutions of ordinary differential equations. Examples of exact solutions anisotropic with respect to the spatial variables are given.
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Kosov et al. (2025) studied this question.