Resurgent trans-series for generalized Hastings–McLeod solutions

Cleri, Nikko J.; Dunne, Gerald V.

doi:10.1088/1751-8121/ab9fb8

Title: Resurgent trans-series for generalized Hastings–McLeod solutions

Abstract

Here, we show that the physical Hastings–McLeod solution of the integrable Painlevé II equation generalizes in a natural way to a class of non-integrable equations, in a way that preserves many of the significant qualitative properties. The Hastings–McLeod solution of Painlevé II is an important and universal example of resurgent relations between perturbative and non-perturbative physics. We derive the trans-series structure of the generalized Hastings–McLeod solutions, demonstrating that integrability is not essential for the resurgent asymptotic properties of the solutions.

Authors:

^[1];

^[1]

Univ. of Connecticut, Storrs, CT (United States)

Publication Date:: Mon Aug 17 00:00:00 EDT 2020

Research Org.:: Univ. of Connecticut, Storrs, CT (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1657613

Grant/Contract Number:: SC0010339

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physics. A, Mathematical and Theoretical

Additional Journal Information:: Journal Volume: 53; Journal Issue: 35; Journal ID: ISSN 1751-8113

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; resurgence; trans-series; Painleve; asymptotics

Citation Formats


                    Cleri, Nikko J., and Dunne, Gerald V. Resurgent trans-series for generalized Hastings–McLeod solutions.  United States: N. p., 2020. 
Web.  doi:10.1088/1751-8121/ab9fb8.

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                    Cleri, Nikko J., & Dunne, Gerald V. Resurgent trans-series for generalized Hastings–McLeod solutions.  United States.  https://doi.org/10.1088/1751-8121/ab9fb8

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                    Cleri, Nikko J., and Dunne, Gerald V. Mon .  
"Resurgent trans-series for generalized Hastings–McLeod solutions".  United States.  https://doi.org/10.1088/1751-8121/ab9fb8.  https://www.osti.gov/servlets/purl/1657613.

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@article{osti_1657613,

  title        = {Resurgent trans-series for generalized Hastings–McLeod solutions},

  author       = {Cleri, Nikko J. and Dunne, Gerald V.},

  abstractNote = {Here, we show that the physical Hastings–McLeod solution of the integrable Painlevé II equation generalizes in a natural way to a class of non-integrable equations, in a way that preserves many of the significant qualitative properties. The Hastings–McLeod solution of Painlevé II is an important and universal example of resurgent relations between perturbative and non-perturbative physics. We derive the trans-series structure of the generalized Hastings–McLeod solutions, demonstrating that integrability is not essential for the resurgent asymptotic properties of the solutions.},

  doi          = {10.1088/1751-8121/ab9fb8},

  journal      = {Journal of Physics. A, Mathematical and Theoretical},

  number       = 35,

  volume       = 53,

  place        = {United States},

  year         = {Mon Aug 17 00:00:00 EDT 2020},

  month        = {Mon Aug 17 00:00:00 EDT 2020}

}

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Works referenced in this record:

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Title: Resurgent trans-series for generalized Hastings–McLeod solutions

Abstract

Citation Formats

Resurgence, Painlevé equations and conformal blocks journal, October 2019

Painlevé transcendents and ${\mathcal{P}}{\mathcal{T}}$-symmetric Hamiltonians journal, October 2015

The Similarity Solution for the Korteweg-de Vries Equation and the Related Painleve Transcendent journal, June 1978

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Asymptotics of the Instantons of Painlevé I journal, March 2011

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Random Unitary Matrices, Permutations and Painlevé journal, November 1999

Hyperasymptotics for Integrals with Saddles journal, September 1991

Non-perturbative contributions in models with a non-analytic behavior at infinite N journal, March 1981

Advanced Mathematical Methods for Scientists and Engineers I book, October 1999

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journal, October 2019

Painlevé transcendents and ${\mathcal{P}}{\mathcal{T}}$-symmetric Hamiltonians
journal, October 2015

The Similarity Solution for the Korteweg-de Vries Equation and the Related Painleve Transcendent
journal, June 1978

Distributions of Poles to Painlevé Transcendents via Padé Approximations
journal, June 2013

Transition asymptotics for the Painlevé II transcendent
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Nonperturbative Ambiguities and the Reality of Resurgent Transseries
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