Novel PTinvariant 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 PTinvariant 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 sech^{2} x, it also admits solutions in terms of the PTinvariant combinations sech^{2} 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 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):
 LAUR1526927
Journal ID: ISSN 03759601; TRN: US1901339
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics Letters. A
 Additional Journal Information:
 Journal Volume: 380; Journal Issue: 78; Journal ID: ISSN 03759601
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Solitons; Nonlinear equations; PTsymmetry
Citation Formats
Khare, Avinash, and Saxena, Avadh. Novel PTinvariant 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 PTinvariant 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 PTinvariant 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 PTinvariant 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 PTinvariant 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 PTinvariant 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 = 78,
volume = 380,
place = {United States},
year = {2015},
month = {12}
}
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Works referencing / citing this record:
Complex PTinvariant 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 PTinvariant 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