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Title: Properties of compacton-anticompacton collisions

Abstract

We study the properties of compacton-anticompacton collision processes. We compare and contrast results for the case of compacton-anticompacton solutions of the K(l,p) Rosenau-Hyman (RH) equation for l=p=2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard-Sodano (CSS) equation for p=1 and l=3. This study is performed using a Pade discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton-anticompacton scattering. For the CSS equation, the scattering can be interpreted as 'annihilation' as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision, which eventually lead to 'blowup' of the resulting wave form.

Authors:
 [1];  [1];  [2];  [3]
  1. Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
  2. Santa Fe Institute, Santa Fe, New Mexico 87501 (United States)
  3. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
Publication Date:
OSTI Identifier:
21554537
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
Additional Journal Information:
Journal Volume: 83; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevE.83.066705; (c) 2011 American Institute of Physics; Journal ID: ISSN 1539-3755
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANNIHILATION; COLLISIONS; COMPARATIVE EVALUATIONS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; SCATTERING; WAVE FORMS; DIFFERENTIAL EQUATIONS; EQUATIONS; EVALUATION; INTERACTIONS; PARTICLE INTERACTIONS

Citation Formats

Cardenas, Andres, Physics Department, New York University, New York, New York 10003, Mihaila, Bogdan, Cooper, Fred, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Saxena, Avadh. Properties of compacton-anticompacton collisions. United States: N. p., 2011. Web. doi:10.1103/PHYSREVE.83.066705.
Cardenas, Andres, Physics Department, New York University, New York, New York 10003, Mihaila, Bogdan, Cooper, Fred, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, & Saxena, Avadh. Properties of compacton-anticompacton collisions. United States. https://doi.org/10.1103/PHYSREVE.83.066705
Cardenas, Andres, Physics Department, New York University, New York, New York 10003, Mihaila, Bogdan, Cooper, Fred, Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Saxena, Avadh. 2011. "Properties of compacton-anticompacton collisions". United States. https://doi.org/10.1103/PHYSREVE.83.066705.
@article{osti_21554537,
title = {Properties of compacton-anticompacton collisions},
author = {Cardenas, Andres and Physics Department, New York University, New York, New York 10003 and Mihaila, Bogdan and Cooper, Fred and Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 and Saxena, Avadh},
abstractNote = {We study the properties of compacton-anticompacton collision processes. We compare and contrast results for the case of compacton-anticompacton solutions of the K(l,p) Rosenau-Hyman (RH) equation for l=p=2, with compacton-anticompacton solutions of the L(l,p) Cooper-Shepard-Sodano (CSS) equation for p=1 and l=3. This study is performed using a Pade discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton-anticompacton scattering. For the CSS equation, the scattering can be interpreted as 'annihilation' as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision, which eventually lead to 'blowup' of the resulting wave form.},
doi = {10.1103/PHYSREVE.83.066705},
url = {https://www.osti.gov/biblio/21554537}, journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
issn = {1539-3755},
number = 6,
volume = 83,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2011},
month = {Wed Jun 15 00:00:00 EDT 2011}
}