Within Gauss–Bonnet gravity, we construct a solution endowed with dyonic matter fields in a higher dimension. The quasi-topological electromagnetism generates two kinds of contributions; one is the kinetic terms, and the second refers to the interactif terms. This overcomes the invariance topological problem. We investigate the thermodynamical proprieties of the obtained solution, namely, ADM mass, Hawking temperature, and entropy. To inspect the local stability, we examine the associated heat capacity. With regards to optical proprieties, we analyze the null geodesic in terms of the given parameter space. The shadow radius is a generating form with all the physical parameters that govern the shadow behavior. The study restricts only the taking of the effects of the D and $$\alpha $$ α parameters. Finally, we examine the impact of the dimension D, GB coupling constant $$\alpha $$ α , the cosmological constant $$\Lambda $$ Λ , the electric $$q_e$$ q e , the magnetic charge $$q_m$$ q m and the coupling constant $$\beta $$ β on the energy emission rate.

While basing on the study that we we achieved on pseudodifferential operators in the works [arXiv:0708.4046 and hep-th/0610056 ], we interest in this paper to the construction of the algebra of -deformed pseudodifferential operators. We use this algebraic structure to study in particular -Burgers and -KdV differential operators by the Lax generating technique. We give -deformed Lax equations as well as the report between these equations through the -deformed Burgers-KdV mapping.

Motivated by string theory results, we study Liouville black hole solutions and their thermodynamics on noncommutative space. In particular, we present explicit solutions of black hole equations of motion, then we find their classical properties such as the ADMmass, the horizon geometry and the scalar Ricci curvature. Thermodynamic properties of such noncommutative black hole solutions including the Hawking temperature and entropy function are also discussed for three different regions of the moduli space of the theory.

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