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:
-
- Savitribai Phule Pune University, Pune (India)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (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:
- Journal Article: 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. https://doi.org/10.1016/j.physleta.2015.12.007
Khare, Avinash, and Saxena, Avadh. 2015.
"Novel PT-invariant solutions for a large number of real nonlinear equations". United States. 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},
url = {https://www.osti.gov/biblio/1457260},
journal = {Physics Letters. A},
issn = {0375-9601},
number = 7-8,
volume = 380,
place = {United States},
year = {Wed Dec 09 00:00:00 EST 2015},
month = {Wed Dec 09 00:00:00 EST 2015}
}
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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
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
Connections Between Complex PT-Invariant Solutions and Complex Periodic Solutions of Several Nonlinear Equations
text, January 2018
- Khare, Avinash; Saxena, Avadh
- arXiv