In this article we find locally an eigenfunctions for a particular nonlinear
hyperbolic differential operator $\Delta_H u^{n}$, where $\Delta_H$ is the
hyperbolic Laplacian in the half-plane of Poincair\’e. We have proved that
these eigenfunctions are an analytic and non-exact whose coefficients satisfy a
specific algebraic recursive rule. The existence of these eigenfunctions allows
us to find non-exact solutions respecting the spatial coordinate of nonlinear
diffusive PDEs on the Poincair\’e half-plane, which could describe a possible
one-dimensional physical model.

Questo articolo esplora i giri e le loro implicazioni.

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