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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

✍ Scribed by A.H. Kara; Ashfaque H. Bokhari

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
193 KB
Volume
16
Category
Article
ISSN
1007-5704

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✦ Synopsis

Saxton and the inviscid Burgers equations a b s t r a c t

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.

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