On a hierarchy of nonlinearly dispersive generalized Korteweg  de Vries evolution equations
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.
 Authors:

^{[1]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
 Publication Date:
 Report Number(s):
 LAUR1520006
Journal ID: ISSN 17366046
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Proceedings of the Estonian Academy of Sciences
 Additional Journal Information:
 Journal Volume: 64; Journal Issue: 3; Journal ID: ISSN 17366046
 Publisher:
 Estonian Academy Publishers
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Korteweg–de Vries equation; compact solitary waves; classical field theory; Lagrangian and Hamiltonian mechanics
 OSTI Identifier:
 1221155
Christov, Ivan C. On a hierarchy of nonlinearly dispersive generalized Korteweg  de Vries evolution equations. United States: N. p.,
Web. doi:10.3176/proc.2015.3.02.
Christov, Ivan C. On a hierarchy of nonlinearly dispersive generalized Korteweg  de Vries evolution equations. United States. doi:10.3176/proc.2015.3.02.
Christov, Ivan C. 2015.
"On a hierarchy of nonlinearly dispersive generalized Korteweg  de Vries evolution equations". United States.
doi:10.3176/proc.2015.3.02. https://www.osti.gov/servlets/purl/1221155.
@article{osti_1221155,
title = {On a hierarchy of nonlinearly dispersive generalized Korteweg  de Vries evolution equations},
author = {Christov, Ivan C.},
abstractNote = {We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.},
doi = {10.3176/proc.2015.3.02},
journal = {Proceedings of the Estonian Academy of Sciences},
number = 3,
volume = 64,
place = {United States},
year = {2015},
month = {8}
}