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):
- 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 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
- Free Publicly Accessible Full Text
-
Accepted Manuscript (DOE)
- Publisher's Version of Record
- https://doi.org/10.3176/proc.2015.3.02