In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

In this article, the generalized Jacobi elliptic function expansion method with four new functions was used to fractional (3 + 1)-dimensional Kadomtsev–Petviashvili (GFKP) equation Atangana-Baleanu-Riemann derivative, and abundant types of analytical solutions GFKP were obtained. It is well known that there a tight connection between symmetry travelling wave solutions. Most existing techniques ...

The class I major histocompatibility complex genes are composed of classical and nonclassical genes, the latter being largely nonfunctional. To understand the evolutionary relationships of the two groups of class I genes, a phylogenetic analysis of DNA sequences was conducted using 45 genes from six mammalian and one avian species. The results indicate that nonclassical genes in one species are...

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints. One of the standard ways for determining particular solutions to partial differential equations is to reduce them to ordinary differential equations which are easier to solve. The classical work of Lie abo...

Charpit’s method of compatibility and the method of nonclassical contact symmetries for first order partial differential equation are considered. It is shown that these two methods are equivalent as Charpit’s method leads to the determining equations arising from the method of nonclassical contact symmetries. Several examples are considered illustrating how Charpit’s method leads quickly and ea...

We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To identify nonclassical processes, we introduce a representation for quantum processes, called the process-nonclassicality quasiprobability distribution, whose ne...

Manipulating the nature of photons emission is one of the basic tasks in quantum optics and photonics. The ever growing list of quantum applications requires a robust means of controlling the strongly coupled coherent interaction of photons and matter. Here, we investigate three-photon transmission spectra in a strongly coupled cavity polariton system and show that the correlation functions and...

We investigate two-color photon correlations in the light emitted by two strongly driven, interacting two-level emitters. The are interpreted introducing collective dressed states picture, which allows us to describe both bunching and antibunching based on allowed prohibited transitions. At odds from weakly emitters, strong interaction lifts degeneracy of energy differences between different st...

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlevé singularity structure analysis singles out a special case (m = 2) as integrable. More interestin...