Symmetries, travelling-wave and self-similar solutions of the Burgers hierarchy

R. Sinuvasan, K.M. Tamizhmani and P.G.L. Leach

Applied Mathematics and Computation, 2017, vol. 303, issue C, 165-170

Abstract: We examine the general element of the Burgers Hierarchy, ut+∂∂x(∂∂x−u)nu=0,n=0,1,2,…, for its Lie point symmetries. We use these symmetries to construct traveling-wave and self-similar solutions. We observe that the general member of the hierarchy can be rendered as a linear (1+1)-evolution equation by means of an elementary Riccati transformation and examine this equation for its Lie point symmetries. With the use of these symmetries we can construct the traveling-wave and self-similar solutions in closed form.

Keywords: Burgers equation; Symmetries; Integrability (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:303:y:2017:i:c:p:165-170

DOI: 10.1016/j.amc.2017.01.036

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