Cosmology and the Korteweg-de Vries Equation

James E. Lidsey

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Cosmology and the Korteweg-de Vries Equation

James E. Lidsey

Cosmology and Nongalactic Astrophysics · Submitted 25 May 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.07 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models. Analogies can be drawn between cosmic dynamics and the propagation of the solitonic wave solution to the equation, whereby quantities such as the speed and amplitude profile of the wave can be identified with cosmological parameters such as the spectral index of the density perturbation spectrum and the energy density of the universe. The unique mathematical properties of the Schwarzian derivative operator are important to the analysis. A connection with dark solitons in Bose-Einstein condensates is briefly discussed.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics.	background 1.00	0.04	0.02	asserted 1.00
s1	In the present paper, we consider its significance to cosmology.	contribution 0.94	0.70	0.03	unclear 0.51
s2	It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models.	result 0.94	0.74	0.43	asserted 1.00
s3	Analogies can be drawn between cosmic dynamics and the propagation of the solitonic wave solution to the equation, whereby quantities such as the speed and amplitude profile of the wave can be identified with cosmological parameters such as the spectral index of the density perturbation spectrum and the energy density of the universe.	result 0.42	0.60	0.37	asserted 0.79
s4	The unique mathematical properties of the Schwarzian derivative operator are important to the analysis.	method 0.72	0.17	0.04	asserted 1.00
s5	A connection with dark solitons in Bose-Einstein condensates is briefly discussed.	contribution 0.72	0.50	0.03	asserted 0.84

What kind of paper the classifier reports this is: review 0.59 · evidence from proof or derivation 0.67.

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arXiv listing abstract v2

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S sections
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has played a fundamental role in diverse branches of mathematical and theoretical physics. In the present paper, we consider its significance to cosmology. It is found that the KdV equation arises in a number of important scenarios, including inflationary cosmology, the cyclic universe, loop quantum cosmology and braneworld models. Analogies can be drawn between cosmic dynamics and the propagation of the solitonic wave solution to the equation, whereby quantities such as the speed and amplitude profile of the wave can be identified with cosmological parameters such as the spectral index of the density perturbation spectrum and the energy density of the universe. The unique mathematical properties of the Schwarzian derivative operator are important to the analysis. A connection with dark solitons in Bose-Einstein condensates is briefly discussed.

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2 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 5 sentences without a confident label

Uses its method or tool 1 paper

Following [ref] , let us assume that the spectral parameter $ł$ is constant.

The KdV in Cosmology: a useful tool or a distraction? · The slow-roll condition and the Schrödinger equation · 0.86

What it cites · 12 sentences without a confident label

Uses data or values from 1 paper

This parameter is bounded from above such that $r < 8(1-n_s)$, which is consistent with the current observational 2$σ$ bound $r<0.24$ [ref] .

Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation · The Inflationary Universe · 0.83

Compares with 1 paper

It is straightforward to verify that these potentials correspond precisely to those derived in [ref] to lowest-order in slow-roll.

Inflationary potentials yielding constant scalar perturbation spectral indices · The Inflationary Universe · 0.95

Cites as support 3 papers

Requiring that the integral of the cosmic energy density (with respect to the scalar field) has a constant Schwarzian derivative led naturally to a modified Friedmann equation that arises generically in the Randall-Sundrum and Shtanov-Sahni braneworld models [ref] and loop quantum cosmology scenarios [ref] .

Bouncing Braneworlds · Discussion · 0.96
Requiring that the integral of the cosmic energy density (with respect to the scalar field) has a constant Schwarzian derivative led naturally to a modified Friedmann equation that arises generically in the Randall-Sundrum and Shtanov-Sahni braneworld models [ref] and loop quantum cosmology scenarios [ref] .

Non-Singular Bouncing Universes in Loop Quantum Cosmology · Discussion · 0.96
Requiring that the integral of the cosmic energy density (with respect to the scalar field) has a constant Schwarzian derivative led naturally to a modified Friedmann equation that arises generically in the Randall-Sundrum and Shtanov-Sahni braneworld models [ref] and loop quantum cosmology scenarios [ref] .

An Alternative to Compactification · Discussion · 0.96

Cites as background 1 paper

The KdV equation has played a central role in diverse branches of physics, including nonlinear optics, atomic and nuclear physics, Bose-Einstein condensates and astrophysical plasmas (see Ref. [ref] for a review.) As far as we are aware, however, it has not been discussed previously within a cosmological context (although see Ref. [ref] ).

Korteweg-de Vries adiabatic index solitons in barotropic open FRW cosmologies · Introduction · 0.97

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