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

doi:10.3176/proc.2015.3.02

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

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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:

Christov, Ivan C. ^[1]

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

Publication Date:: 2015-08-20

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


                    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.

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                    Christov, Ivan C. On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations.  United States.  doi:10.3176/proc.2015.3.02.

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                    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.

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@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}

}

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10.3176/proc.2015.3.02
https://doi.org/10.3176/proc.2015.3.02

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

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