On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations

Journal Article · Thu Aug 20 00:00:00 EDT 2015 · Proceedings of the Estonian Academy of Sciences

DOI:https://doi.org/10.3176/proc.2015.3.02· OSTI ID:1221155

Christov, Ivan C. ^[1]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division and Center for Nonlinear Studies

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.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1221155
• Report Number(s): LA-UR-15-20006
• Journal Information: Proceedings of the Estonian Academy of Sciences, Vol. 64, Issue 3; ISSN 1736-6046
• Publisher: Estonian Academy Publishers
• Country of Publication: United States
• Language: English

Related Subjects

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