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Title: 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 Vries-type models. Peakompactons, like the now-well-known 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 phase-plane analysis. Lastly, a simple, but reliable, finite-difference 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 so-called K #(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.

Authors:
 [1];  [2]; ORCiD logo [3]
  1. Purdue Univ., West Lafayette, IN (United States)
  2. Univ. of North Carolina, Chapel Hill, NC (United States)
  3. 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):
LA-UR-16-27517
Journal ID: ISSN 0217-9792
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
International Journal of Modern Physics B
Additional Journal Information:
Journal Volume: 31; Journal Issue: 10; Journal ID: ISSN 0217-9792
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 Vries-type models. Peakompactons, like the now-well-known 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 phase-plane analysis. Lastly, a simple, but reliable, finite-difference 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 so-called K#(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.},
doi = {10.1142/S0217979217420085},
journal = {International Journal of Modern Physics B},
number = 10,
volume = 31,
place = {United States},
year = {2017},
month = {4}
}

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