Classifying Exact Traveling Wave Solutions to the Coupled-Higgs Equation

Ji-ying, Liu

doi:10.4236/jamp.2015.33041

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…bifurcation in optical fibres [7] and the interaction of wave elements [8] including rogue waves [9]. This approach provides a mathematical model for nonlinear behaviours [10], typically using a polynomial complete discriminant method [11] [12] [13] and has primarily been applied to wave propagation effects, optical as well as water, but also other effects such as nerve signal propagation [14]. While mathematically powerful and able to model complex wave phenomena, this approach does not appear to have resulted in an explicit derivation for the Fresnel equations.…”

Section: Introductionmentioning

confidence: 99%

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Pons

2024

JMP

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Problem: The Fresnel equations describe the proportions of reflected and transmitted light from a surface, and are conventionally derived from wave theory continuum mechanics. Particle-based derivations of the Fresnel equations appear not to exist. Approach: The objective of this work was to derive the basic optical laws from first principles from a particle basis. The particle model used was the Cordus theory, a type of non-local hidden-variable (NLHV) theory that predicts specific substructures to the photon and other particles. Findings: The theory explains the origin of the orthogonal electrostatic and magnetic fields, and re-derives the refraction and reflection laws including Snell's law and critical angle, and the Fresnel equations for s and p-polarisation. These formulations are identical to those produced by electromagnetic wave theory. Contribution: The work provides a comprehensive derivation and physical explanation of the basic optical laws, which appears not to have previously been shown from a particle basis. Implications: The primary implications are for suggesting routes for the theoretical advancement of fundamental physics. The Cordus NLHV particle theory explains optical phenomena, yet it also explains other physical phenomena including some otherwise only accessible through quantum mechanics (such as the electron spin g-factor) and general relativity (including the Lorentz and relativistic Doppler). It also provides solutions for phenomena of unknown causation, such as asymmetrical baryogenesis, unification of the interactions, and reasons for nuclide stability/instability. Consequently, the implication is that NLHV theories have the potential to represent a deeper physics that may underpin and unify quantum mechanics, general relativity, and wave theory.

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Section: Introductionmentioning

confidence: 99%

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Pons

2024

JMP

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“…Several attempts by different scientists have been made to investigate Eq. (1.2) [64][65][66][67][68][69][70][71].…”

Section: Introductionmentioning

confidence: 99%

On the exact solutions to some system of complex nonlinear models

Sulaıman

Bulut

Başkonuş

2020

Applied Mathematics and Nonlinear Sciences

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In this manuscript, the application of the extended sinh-Gordon equation expansion method to the Davey-Stewartson equation and the (2+1)-dimensional nonlinear complex coupled Maccari system is presented. The Davey-Stewartson equation arises as a result of multiple-scale analysis of modulated nonlinear surface gravity waves propagating over a horizontal seabed and the (2+1)-dimensional nonlinear complex coupled Maccari equation describes the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics. We successfully construct some soliton, singular soliton and singular periodic wave solutions to these two nonlinear complex models. The 2D, 3D and contour graphs to some of the obtained solutions are presented.

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“…Literature [1]- [9] obtained new finite one-soliton solutions of Schrödinger equation. Based on the auxiliary equation method [10]- [24], the paper constructs the new infinite sequence composite exact solutions of a kind of coupled Schrödinger equation.…”

Section: Introductionmentioning

confidence: 99%

Some Kinds of New Composite Solutions of a Kind of Coupled Schrödinger Equation

Na¹,

Dong²,

Taogetusang³

2015

JAMP

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With the help of the method that combines the first kind of elliptic equation with the function transformation, some kinds of new composite solutions of a kind of coupled Schrödinger equation are constructed. First, a kind of function transformation is presented, and then the problem of solving solutions of a kind of coupled Schrödinger equation can be changed to the problem of solving solutions of the first kind of elliptic equation. Then, with the help of the conclusions of the Bäcklund transformation and so on of the first kind of elliptic equation, the new infinite sequence composite solutions of a kind of coupled Schrödinger equation are constructed. These solutions are consisting of two-soliton solutions and two-period solutions and so on.

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Classifying Exact Traveling Wave Solutions to the Coupled-Higgs Equation

Abstract: By the complete discrimination system for polynomials, we classify exact traveling wave solutions to the Coupled-Higgs Equation.

Cited by 4 publications

References 6 publications

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

On the exact solutions to some system of complex nonlinear models

Some Kinds of New Composite Solutions of a Kind of Coupled Schrödinger Equation

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Classifying Exact Traveling Wave Solutions to the Coupled-Higgs Equation

Abstract: By the complete discrimination system for polynomials, we classify exact traveling wave solutions to the Coupled-Higgs Equation.

Cited by 4 publications

References 6 publications

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

On the exact solutions to some system of complex nonlinear models

Some Kinds of New Composite Solutions of a Kind of Coupled Schr&#246;dinger Equation

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Product

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About

Some Kinds of New Composite Solutions of a Kind of Coupled Schrödinger Equation