On multi-solitons for coupled Lowest Landau Level equations

Laurent Thomann (IECL)

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On multi-solitons for coupled Lowest Landau Level equations

Laurent Thomann (IECL)

Analysis of PDEs · Submitted 9 Nov 2021

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

The authors' main claim We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,574 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.69 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.06 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We consider a coupled system of nonlinear Lowest Landau Level equations. We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result. We also show a long time stability result of the sum of traveling waves having all the same speed, under the condition that they are localised far away enough from each other. Finally, we observe that these multi-solitons provide examples of dynamics for the linear Schr{\"o}dinger equation with harmonic potential perturbed by a time-dependent potential.

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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	We consider a coupled system of nonlinear Lowest Landau Level equations.	background 0.73	0.57	0.04	asserted 0.75
s1	We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result.	result 0.69	0.97	0.57	asserted 1.00
s2	We also show a long time stability result of the sum of traveling waves having all the same speed, under the condition that they are localised far away enough from each other.	result 0.96	0.95	0.17	asserted 1.00
s3	Finally, we observe that these multi-solitons provide examples of dynamics for the linear Schr{\"o}dinger equation with harmonic potential perturbed by a time-dependent potential.	interpretation 0.82	0.90	0.14	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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The paper

Original abstract

We consider a coupled system of nonlinear Lowest Landau Level equations. We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result. We also show a long time stability result of the sum of traveling waves having all the same speed, under the condition that they are localised far away enough from each other. Finally, we observe that these multi-solitons provide examples of dynamics for the linear Schr{\"o}dinger equation with harmonic potential perturbed by a time-dependent potential.

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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

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Next by [ref] , there exists $r_0 ∈𝒞(; ^1())$ which satisfies [equation] and such that [equation] is solution to the equation [ref].

On weakly turbulent solutions to the perturbed linear Harmonic oscillator · Proof of Theorem [ref] · 0.81

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