A non-variational approach to the construction of new 'higher-order' conservation laws of the family of nonlinear equations α(ut+3uux)+β(utxx+2uxuxx+uuxxx)-γuxxx=0

A. H. Kara; Ashfaque H. Bokhari

doi:10.1016/j.cnsns.2011.03.007

A non-variational approach to the construction of new 'higher-order' conservation laws of the family of nonlinear equations α(u_t+3uu_x)+β(u_txx+2u_xu_xx+uu_xxx)-γu_xxx=0

A. H. Kara^*
, Ashfaque H. Bokhari

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study and classify the conservation laws of the combined nonlinear KdV, Camassa-Holm, Hunter-Saxton and the inviscid Burgers equation which arises in, inter alia, shallow water equations. It is shown that these can be obtained by variational methods but the main focus of the paper is the construction of the conservation laws as a consequence of the interplay between symmetry generators and 'multipliers', particularly, the higher-order ones.

Original language	English
Pages (from-to)	4183-4188
Number of pages	6
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	16
Issue number	11
DOIs	https://doi.org/10.1016/j.cnsns.2011.03.007
State	Published - Nov 2011

Keywords

Camassa-Holm
Hunter-Saxton and the inviscid Burgers equations
Non-variational method for conservation laws

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Applied Mathematics

Access to Document

10.1016/j.cnsns.2011.03.007

Cite this

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title = "A non-variational approach to the construction of new 'higher-order' conservation laws of the family of nonlinear equations α(ut+3uux)+β(utxx+2uxuxx+uuxxx)-γuxxx=0",

abstract = "In this paper, we study and classify the conservation laws of the combined nonlinear KdV, Camassa-Holm, Hunter-Saxton and the inviscid Burgers equation which arises in, inter alia, shallow water equations. It is shown that these can be obtained by variational methods but the main focus of the paper is the construction of the conservation laws as a consequence of the interplay between symmetry generators and 'multipliers', particularly, the higher-order ones.",

keywords = "Camassa-Holm, Hunter-Saxton and the inviscid Burgers equations, Non-variational method for conservation laws",

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pages = "4183--4188",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier B.V.",

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}

A non-variational approach to the construction of new 'higher-order' conservation laws of the family of nonlinear equations α(u_t+3uu_x)+β(u_txx+2u_xu_xx+uu_xxx)-γu_xxx=0. / Kara, A. H.; Bokhari, Ashfaque H.
In: Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 11, 11.2011, p. 4183-4188.

Research output: Contribution to journal › Article › peer-review

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AU - Bokhari, Ashfaque H.

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KW - Camassa-Holm

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KW - Non-variational method for conservation laws

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