Peakompactons: Peaked compact nonlinear waves
Abstract
This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vriestype models. Peakompactons, like the nowwellknown compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly by reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phaseplane analysis. Lastly, a simple, but reliable, finitedifference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the socalled K ^{#}(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vriestype models are discussed as well.
 Authors:
 Purdue Univ., West Lafayette, IN (United States)
 Univ. of North Carolina, Chapel Hill, NC (United States)
 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 National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1356135
 Report Number(s):
 LAUR1627517
Journal ID: ISSN 02179792
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 International Journal of Modern Physics B
 Additional Journal Information:
 Journal Volume: 31; Journal Issue: 10; Journal ID: ISSN 02179792
 Publisher:
 World Scientific
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING; Mathematics
Citation Formats
Christov, Ivan C., Kress, Tyler, and Saxena, Avadh. Peakompactons: Peaked compact nonlinear waves. United States: N. p., 2017.
Web. doi:10.1142/S0217979217420085.
Christov, Ivan C., Kress, Tyler, & Saxena, Avadh. Peakompactons: Peaked compact nonlinear waves. United States. doi:10.1142/S0217979217420085.
Christov, Ivan C., Kress, Tyler, and Saxena, Avadh. Thu .
"Peakompactons: Peaked compact nonlinear waves". United States.
doi:10.1142/S0217979217420085. https://www.osti.gov/servlets/purl/1356135.
@article{osti_1356135,
title = {Peakompactons: Peaked compact nonlinear waves},
author = {Christov, Ivan C. and Kress, Tyler and Saxena, Avadh},
abstractNote = {This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vriestype models. Peakompactons, like the nowwellknown compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly by reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phaseplane analysis. Lastly, a simple, but reliable, finitedifference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the socalled K#(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vriestype models are discussed as well.},
doi = {10.1142/S0217979217420085},
journal = {International Journal of Modern Physics B},
number = 10,
volume = 31,
place = {United States},
year = {Thu Apr 20 00:00:00 EDT 2017},
month = {Thu Apr 20 00:00:00 EDT 2017}
}

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