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Algebraic resolution of the Burgers equation with a forcing term

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Abstract

We introduce an inhomogeneous term, f(t,x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f(t,x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra s l(2,R). When f is a function of only t, there are five symmetries with the algebra s l(2,R) ⊕ s 2A 1. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.

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Acknowledgements

R Sinuvasan thanks the University Grants Commission for its support. PGLL thanks Professor K M Tamizhmani and the Department of Mathematics, Pondicherry University, for providing facilities whilst this work was undertaken. PGLL also thanks the University of KwaZulu-Natal and the National Research Foundation of the Republic of South Africa for their continued support. Any views expressed in this paper are not necessarily those of the two institutions.

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Authors and Affiliations

  1. Department of Mathematics, Pondicherry University, Kalapet, 605 014, India

    R SINUVASAN, K M TAMIZHMANI & P G L LEACH

  2. Permanent addresses: School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, Republic of South Africa and Institute for Systems Science, Department of Mathematics, Durban University of Technology, P.O. Box 1334, Durban, 4000, Republic of South Africa

    P G L LEACH

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  1. R SINUVASAN
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  3. P G L LEACH
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Correspondence to R SINUVASAN.

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SINUVASAN, R., TAMIZHMANI, K.M. & L LEACH, P.G. Algebraic resolution of the Burgers equation with a forcing term. Pramana - J Phys 88, 74 (2017). https://doi.org/10.1007/s12043-017-1382-3

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  • DOI: https://doi.org/10.1007/s12043-017-1382-3

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