Mathematical Physics

2011 Submissions

[9] viXra:2011.0187 [pdf] submitted on 2020-11-27 10:35:58

On Polynomial Differential Equations of Duffing Type

Authors: M. D. Monsia
Comments: 3 Pages.

The exact and explicit general periodic solution of polynomial differential equations of Duffing type is calculated as a power law of the cosine function. In doing so the solution of all Duffing equations of three terms like the cubic, quintic and heptic equations may be easily expressed in a straightforward fashion.
Category: Mathematical Physics

[8] viXra:2011.0132 [pdf] replaced on 2021-07-18 18:31:06

An Attempt to Approach Mathematically the Concept of Time-Crystals

Authors: Udo E. Steinemann
Comments: 12 Pages.

F. WILCZEK has published an article on the concept of time-crystals (please look into [1]). This article is to be understood as an attempt to drawn a picture mathematically, which approaches the contents of WILCZEK’s article.
Category: Mathematical Physics

[7] viXra:2011.0111 [pdf] submitted on 2020-11-15 11:49:40

Similar to the Magic Angle Formula of Graphene Magic Angle

Authors: Huang Shan
Comments: 1 Page.

By speculating the magic angle of graphene, we can guess the magic angle formula of other crystals.
Category: Mathematical Physics

[6] viXra:2011.0110 [pdf] submitted on 2020-11-15 11:49:53

Deducing the Relationship Between Physical Constants from the Numerical Values of Physical Constants

Authors: Huang Shan
Comments: 1 Page.

Other basic physical constants can be derived as long as the speed of light, the value of the basic charge, and the value of one of the two vacuum permeability and vacuum permittivity are known.
Category: Mathematical Physics

[5] viXra:2011.0105 [pdf] submitted on 2020-11-13 23:14:49

Differentials as Tensors and the Taylor Series

Authors: Anamitra Palit
Comments: 7 Pages.

The article considers tensor transformations of the differential elements pertaining to the coordinates to derive that the nth order differential behaves as a tensor. This stands in contradiction to accepted notions. It also derives by considering the Taylor series, a significant and an unexpectedly conflicting result that the nth order partial derivatives of scalar functions with respect to the coordinates behave like rank ‘n‘covariant tensors.
Category: Mathematical Physics

[4] viXra:2011.0079 [pdf] submitted on 2020-11-11 08:42:32

Solutions of the Navier-Stokes Equations

Authors: Antoine Balan
Comments: 2 Pages.

We geometrize the Navier-Stokes equations and we propose a Lagrangian to solve the NS equations.
Category: Mathematical Physics

[3] viXra:2011.0059 [pdf] replaced on 2020-11-20 21:11:31

On a Differential Equation of Lienard Type with Strong Nonlinearities

Authors: M. D. Monsia
Comments: 8 Pages.

In this paper we present a remarkable Lienard equation with strong and high order nonlinear terms. The equation is explicitly integrable in terms of periodic tangent function. The related quadratic Lienard type equations may also exhibit the tangent function profile. The presented equation includes for example, the cubic and quintic Duffing equations with cubic singularity as special cases.
Category: Mathematical Physics

[2] viXra:2011.0050 [pdf] replaced on 2020-11-11 19:15:25

On a Nonlinear Differential Equation of Lienard Type

Authors: M. D. Monsia
Comments: 7 pages

We present, in this paper, an exceptional Lienard differential equation. In spite of the presence of strong and high order nonlinearity term, the proposed equation is explicitly integrable. The general solution is expressed in terms of trigonometric functions. Also the general solutions of related quadratic Lienard type equations are periodic and may exhibit harmonic oscillations. The presented equation includes many nonlinear equations like the cubic-quintic, and cubic Duffing equations, Mickens truly nonlinear equations and the Ermakov-Pinney equation as special cases so that the explicit general solution of several nonlinear equations may be easily obtained for the first time.
Category: Mathematical Physics

[1] viXra:2011.0041 [pdf] submitted on 2020-11-05 19:51:05

On the General Solutions of Lienard Equations with Strong Nonlinearities

Authors: M. D. Monsia
Comments: 7 Pages.

We derive the Lienard equation with strong nonlinearities from the solution of the Ermakov-Pinney equation. As a result, we give the exact and explicit general solution of this equation for the first time, so that the solution of a lot of differential equations like the cubic-quintic Duffing equation may be easily obtained.
Category: Mathematical Physics