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Title: 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]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies
Publication Date:
OSTI Identifier:
1221155
Report Number(s):
LA-UR--15-20006
Journal ID: ISSN 1736-6046
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Proceedings of the Estonian Academy of Sciences
Additional Journal Information:
Journal Volume: 64; Journal Issue: 3; Journal ID: ISSN 1736-6046
Publisher:
Estonian Academy Publishers
Research Org:
Los Alamos National Laboratory (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