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Gain of regularity for a coupled system of generalized nonlinear Schr\"odinger equations

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Raul Nina Mollisaca, Mauricio Sepúlveda Cortés, Rodrigo Véjar Asem, Octavio Vera Villagrán

Analysis of PDEs · Submitted 18 Jan 2023

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

The authors' main claim We show that the equations dispersive nature leads to a gain in regularity for the solution.

how it is stated · asserted 1.00 read the record →

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arXiv ID2301.07816 (version 1)
Pith ID2EYCT2ZF, Pith's permanent record of this paper and its review
CitationMauricio Sep\'ulveda Cort\'es, Octavio Vera Villagr\'an, Raul Nina Mollisaca, Rodrigo V\'ejar Asem. "Gain of regularity for a coupled system of generalized nonlinear Schr\"odinger equations." arXiv:2301.07816 (2023). https://pith.science/paper/2EYCT2ZF
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,134 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schr\"{o}dinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr medium in nonlinear optics. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data $(u_{0},\,v_{0})$ possesses certain regularity and sufficient decay as $|x|\rightarrow\infty,$ then the solution $(u(t),\,v(t))$ will be smoother than $(u_{0},\,v_{0})$ for $0 < t \leq T$ where $T$ is the existence time of the solution.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schr\"{o}dinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr medium in nonlinear optics. contribution 0.67 0.61 0.04 asserted 0.93
s1 We show that the equations dispersive nature leads to a gain in regularity for the solution. result 0.90 0.93 0.79 asserted 1.00
s2 In particular, if the initial data $(u_{0},\,v_{0})$ possesses certain regularity and sufficient decay as $|x|\rightarrow\infty,$ then the solution $(u(t),\,v(t))$ will be smoother than $(u_{0},\,v_{0})$ for $0 < t \leq T$ where $T$ is the existence time of the solution. result 1.00 0.89 0.77 asserted 0.80

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

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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

In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schr\"{o}dinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr medium in nonlinear optics. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data $(u_{0},\,v_{0})$ possesses certain regularity and sufficient decay as $|x|\rightarrow\infty,$ then the solution $(u(t),\,v(t))$ will be smoother than $(u_{0},\,v_{0})$ for $0 < t \leq T$ where $T$ is the existence time of the solution.

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