Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0503194

Geometric Solutions to Non-linear Differential Equations

Gordon Chalmers
View original source ↗Read source document ↗Export metadata ↓

Abstract

A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves generic nonlinear systems. Further properties characterized by the topology and geometry of the associated manifolds may define global properties of the solutions.

Explore related subjects

physics.gen-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gordon Chalmers. 2005-03-25. Geometric Solutions to Non-linear Differential Equations. https://arxiv.org/abs/physics/0503194

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

"The Information as Absolute" Concept and Basic Physics

This paper is the presentation of the 2007-2026 Planck scale informational physical model, which is based on philosophical "The Information as Absolute" concept, which was formulated mainly in 2007. In the concept it is rigorously proven that nothing exists besides some informational patterns/systems of the patterns that are elements of the absolutely fundamental, and absolutely infinite, "Information" Set. Thus Matter for sure is nothing else than some informational system of informational patterns (sub-systems) - particles, fields, bodies, etc. The other fundamental base of the model is the outstanding findings of von Weizsacker and Fredkin-Toffli, who proved that Matter is based on some binary logics ("UR hypothesis"), and that if a system consists of reversible elements, then this system doesn't dissipate energy outside, whereas the conception above makes these findings as completely natural. That allowed to define scientifically a number of fundamental phenomena/notions, first of all "Space", "Time", "Matter", "Energy", "Inertia", and so to solve, or essentially to clarify, a number of fundamental physical problems, considering everything in Matter as some specific disturbances in Matter's ultimate base - dense lattice of fundamental logical elements (FLE) that is placed in real Matter(here utmost universal "kinematical") [5]4D spacetime) - what are particles and antiparticles, what are physical senses of basic equations ib kinematics, first of all of Lorents transformations and in dynamics., etc.

physics.gen-ph↗
arXiv2026

Two-Time Relativistic Bohmian Model of Quantum Mechanics

Two-Time relativistic Bohmian Model (TTBM) is a theory in which the apparently paradoxical aspects of Quantum Mechanics are the effect of the existence of an extra unobservable time dimension. The hypothesis that matter is capable of motion with respect to an additional independent time (thus resulting instantaneous with respect to usual time) is capable of restoring determinism, explaining the Zitterbewegung without evoking virtual antimatter. The model also predicts a relativistic correction of the uncertainty principle. Here the model is first summarized (definition, salient properties and empiricism) and after applied to a generic spherical atomic orbit, obtaining electron oscillations in the new time dimension, tau, which demonstrate the static nature of the orbitals. Something very similar happens in the case of a particle in a box, where tau-oscillations cause the particle to spread out at steady states. Some astrophysical and about spin speculations follow. Finally, it is discussed how the model fits into the fundamental problem of the definition of time in Quantum Mechanics. Keywords: Quantum Mechanics Foundations; de Broglie-Bohm Theory; Zitterbewegung; Uncertainty principle verification; Extra dimensions; Atomic orbitals; Spin; Definition of time in Quantum Mechanics.

physics.gen-ph↗
arXiv2026

Joss-Weinberg covariant field with mass and spin 3/2

We present the explicit theory of the Joss-Weinberg covariant field with spin $\frac{3}{2}$ which is a eight-dimensional massive covariant field transforming according to the representation $(\frac{3}{2},0)\oplus(0, \frac{3}{2})$ of the group $SL(2,\mathbb{C})$. As the transformation matrices of this representation are still unknown, we apply a new method for deriving them using exclusively maximally reducible representations, e. g. $(1,0)\otimes(\frac{1}{2},0)$ instead of the irreducible one $(1,\frac{1}{2})=(1,0)\otimes(0,\frac{1}{2})$ we meet in usual frameworks. After applying this method, we obtain a $12$-component covariant field transforming according to the representation $[(1,0)\otimes(\frac{1}{2},0)]\oplus [(0,1)\otimes(0, \frac{1}{2})]$ which is maximally reducible, up to subspaces of irreducible representations of the $SU(2)$ group. Consequently, after developing the theory in the direct product basis of the representation $(1,0)\otimes(\frac{1}{2},0)$, we can separate the sector of spin half revealing thus the genuine Joss-Weinberg covariant field of spin $\frac{3}{2}$, transforming according to the representation $(\frac{3}{2},0)\oplus(0, \frac{3}{2})$. In this manner the theory of Joss-Weinberg covariant field of spin $\frac{3}{2}$ can be build naturally deriving the field equation and associated matrices, Lagrangian formalism, inner product and the closed expressions of the orthonormal mode spinors.

physics.gen-ph↗