aqora

The Prince Wave Equation A Rigorous Derivation from the de Broglie Relation on the Euler Complex Plane

Mustafa A Khan

Jul 31, 20260 citations

Propagation of nonlinear de Broglie waves in four-dimensional space and the sine-Gordon equation

Partha Pratim Mukhopadhyay

Physics Letters AMar 1, 19881 citation

The Nonlinear de Broglie Wave Equation in the Prince Frame: A Complete Derivation from the Work Equation and the de Broglie Relation

Mustafa Khan

We derive the nonlinear de Broglie wave equation inthe Prince Frame from the work equation, the deBroglie relation λp = h, and the geometry of theEuler Complex Plane (ECP). The separation of spatialand temporal components of the wavefunctionarises naturally from the ECP, where the spatial compactionfield ψ(λi) is multiplied by the Euler oscillatore±iωt. The Prince Frame provides the coupledspatial Laplacian, while the ECP provides the nonlinearself-interaction term 8π^2{v(g)}^2|ψ|^2 ψ. The resultis a fully derived geometric wave equation with noempirical inputs.We derive the nonlinear de Broglie wave equation inthe Prince Frame from the work equation, the deBroglie relation λp = h, and the geometry of theEuler Complex Plane (ECP). The separation of spatialand temporal components of the wavefunctionarises naturally from the ECP, where the spatial compactionfield ψ(λi) is multiplied by the Euler oscillatore±iωt. The Prince Frame provides the coupledspatial Laplacian, while the ECP provides the nonlinearself-interaction term 8π^2{v(g)}^2|ψ|^2 ψ. The resultis a fully derived geometric wave equation with noempirical inputs.

Aug 17, 20260 citations

Recent Progress in De Broglie Nonlinear Wave Mechanics

Ph. Gueret

Springer eBooksJan 1, 19850 citations

The Generalized Prince Wave Equation on the Euler Complex Plane: A Complete Derivation from the de Broglie Relation.

Mustafa Khan

We derive the generalized nonlinear wave equation for a matter wave on theEuler Complex Plane (ECP), using only the de Broglie relation λp = h and theECP geometry. The wavefunction is taken as Ψ(r, θ, t) = ψ(r, θ)e±iωt, where ψ(r, θ)is the spatial compaction field and e±iωt is the Euler oscillator. The derivation usesthe Prince Razor δp = hδψ, the work-energy theorem dE = v dp, and the localphase harmony condition dτ = dt. The result is a fully general nonlinear waveequation that includes radial and angular derivatives, cross terms, and accelerationterms. It reduces to the standard Prince wave equation in the static radial limit.The equation is defined entirely on the ECP and contains no empirical inputs. It issuitable for application to fluid dynamics, including the Navier-Stokes problem, asthe ECP geometry naturally prevents singularities.We derive the generalized nonlinear wave equation for a matter wave on theEuler Complex Plane (ECP), using only the de Broglie relation λp = h and theECP geometry. The wavefunction is taken as Ψ(r, θ, t) = ψ(r, θ)e±iωt, where ψ(r, θ)is the spatial compaction field and e±iωt is the Euler oscillator. The derivation usesthe Prince Razor δp = hδψ, the work-energy theorem dE = v dp, and the localphase harmony condition dτ = dt. The result is a fully general nonlinear waveequation that includes radial and angular derivatives, cross terms, and accelerationterms. It reduces to the standard Prince wave equation in the static radial limit.The equation is defined entirely on the ECP and contains no empirical inputs. It issuitable for application to fluid dynamics, including the Navier-Stokes problem, asthe ECP geometry naturally prevents singularities.

Aug 3, 20260 citations

ON PHYSICAL INTERPRETATION OF De BROGLIE EQUATIONS

I.I. Kobozev

Russian Journal of Physical Chemistry AJan 1, 19550 citations

The Nonlinear de Broglie Wave Equation in the Prince Frame: A Complete Derivation from the Work Equation and the de Broglie Relation

Related papers

The Nonlinear de Broglie Wave Equation in the Prince Frame: A Complete Derivation from the Work Equation and the de Broglie Relation

Related papers