Physical Mathematics

The problem solution is constructed for the homogeneous case of the co-efficient of permeability. In the case of a variable concentration obtained by changing the salt content, neutral representations are obtained that allow us to determine the main hydrodynamic parameters of the filtration process.

I come from a medical background. I haven't seriously studied physics since high school but I like to observe things and I like the mysteries of quantum mechanics. Solving mysteries is one of the most important approaches to the development of humanity. With that said I would like to propose here where to look for solutions for one of the most important mysteries of quantum mechanics. The double-slit experiment.

This paper is considred to solve one-dimensional diffusion equation with nonlinear nonlocal boundary conditions. For the interior part of the problem, our discrete methods use the Forward time centred space (FTCS-NNC), Dufort–Frankel scheme (DFS-NNC), Backward time centred space (BTCS-NNC), Crank-Nicholson method (CNM-NNC), respectively. The integrals in the boundary equations are approximated by the trapezoidal rule. Here nonlinear terms are approximated by Richtmyer’s linearization method. The new algorithm are tested on two problems to show the effciency and accuracy of the schemes.

Construction of super NLPDE’s is performed to the aim of finding novel dynamic evolution equations that describe highly dispersive nonlinear systems. It is found that a coupled NLPDE generates a super NLPDE. Which may reveal novel nonlinear phenomena and provide an interpretation of the phenomena complexity. Attention is focused to find the super formulation of the nonlinear, coupled nonlinear Schrodinger (NLS, CNLS), Davey-Stwartson (generalized Zakharov), Higg’s, and coupled KdV equations. The CNLS equation may help to control the propagation of soliton (pulse) waves in fiber optics. These equations are currently used in engineering such as the management of the concept of soliton in the development of modern technology via the study of Bose-Einstein condensate phenomena. Further, to test the behavior and study the characteristics of the propagation of laser pulse and high-power fiber laser applications. Here, the extended unified method is used to find the solutions of the traveling wave to the super KdV equation. These solutions show solitary, soliton with double kinks waves and lumps. We think that the novel equations constructed here will open a new trend of research that may lead new phenomena in the applied sciences.

A mathematical cliff consists of scalar, vector and spinor, while scalar, vector and spinor are cliff components. It is found that the static exchange product of cliff components produces quantum, such as exchange multiplication of scalar and vector [X, Y]=XY–YX = ℏ/i, and that the complex dynamic distribution of i(z) as logarithm of negative numbers is just probability density, yielding quantum statistical mechanism. The mathematical principle reveals physical implications characterized by static “one cliff, one state” and dynamic “i(z) generates probability”, where the complex conjugation of the cliff indicates entangled one, resembling a concise mathematical principle of quantum mechanism. While the inner relations among scalars, vectors and spinors reveal local laws, the outer relations between cliffs describe global laws, leading to harmonic mathematical physics.