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Title: Novel PT-invariant solutions for a large number of real nonlinear equations

Abstract

We report that for a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, we show that whenever a real nonlinear equation admits a solution in terms of sech x, it also admits solutions in terms of the PT-invariant combinations sech x ± i tanh x. Additionally, for a number of real nonlinear equations we show that whenever a nonlinear equation admits a solution in terms sech2 x, it also admits solutions in terms of the PT-invariant combinations sech2 x ± i sech x tanh x. Besides, we show that similar results are also true in the periodic case involving Jacobi elliptic functions.

Authors:
 [1]; ORCiD logo [2]
  1. Savitribai Phule Pune University, Pune (India)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1457260
Alternate Identifier(s):
OSTI ID: 1246552
Report Number(s):
LA-UR-15-26927
Journal ID: ISSN 0375-9601; TRN: US1901339
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physics Letters. A
Additional Journal Information:
Journal Volume: 380; Journal Issue: 7-8; Journal ID: ISSN 0375-9601
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Solitons; Nonlinear equations; PT-symmetry

Citation Formats

Khare, Avinash, and Saxena, Avadh. Novel PT-invariant solutions for a large number of real nonlinear equations. United States: N. p., 2015. Web. doi:10.1016/j.physleta.2015.12.007.
Khare, Avinash, & Saxena, Avadh. Novel PT-invariant solutions for a large number of real nonlinear equations. United States. doi:https://doi.org/10.1016/j.physleta.2015.12.007
Khare, Avinash, and Saxena, Avadh. Wed . "Novel PT-invariant solutions for a large number of real nonlinear equations". United States. doi:https://doi.org/10.1016/j.physleta.2015.12.007. https://www.osti.gov/servlets/purl/1457260.
@article{osti_1457260,
title = {Novel PT-invariant solutions for a large number of real nonlinear equations},
author = {Khare, Avinash and Saxena, Avadh},
abstractNote = {We report that for a large number of real nonlinear equations, either continuous or discrete, integrable or nonintegrable, we show that whenever a real nonlinear equation admits a solution in terms of sech x, it also admits solutions in terms of the PT-invariant combinations sech x ± i tanh x. Additionally, for a number of real nonlinear equations we show that whenever a nonlinear equation admits a solution in terms sech2 x, it also admits solutions in terms of the PT-invariant combinations sech2 x ± i sech x tanh x. Besides, we show that similar results are also true in the periodic case involving Jacobi elliptic functions.},
doi = {10.1016/j.physleta.2015.12.007},
journal = {Physics Letters. A},
number = 7-8,
volume = 380,
place = {United States},
year = {2015},
month = {12}
}

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Works referencing / citing this record:

Complex PT-invariant cnoidal and hyperbolic solutions of several real nonlinear equations
journal, April 2018

  • Khare, Avinash; Saxena, Avadh
  • Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 17
  • DOI: 10.1088/1751-8121/aab4d8

Connections between complex PT-invariant solutions and complex periodic solutions of several nonlinear equations
journal, October 2019

  • Khare, Avinash; Saxena, Avadh
  • Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 46
  • DOI: 10.1088/1751-8121/ab4a33