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Application of Group Methods in Solving Wave Equations

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Proceedings of the Seventh International Conference on Mathematics and Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1412))

Abstract

We obtain the Lie invariance condition for partial differential equations of second order. This condition is used in obtaining the determining equations of the one-dimensional wave equation with constant speed. The determining equations are split to obtain an overdetermined system of partial differential equations, which are solved to obtain the symmetries of the wave equation. By making an appropriate transformation between the dependent and independent variables, the wave equation is reduced to an easily solvable ordinary differential equation. We solve this resulting differential equation to obtain the solutions of the wave equation. In particular, the one-dimensional wave equation with unit speed has been solved.

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Author information

Authors and Affiliations

  1. Department of Mathematics, St. Xavier’s College, Mapusa, Goa, India

    Jervin Zen Lobo

Authors
  1. Jervin Zen Lobo
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Editor information

Editors and Affiliations

  1. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  2. The University of Texas at San Antonio, San Antonio, TX, USA

    Kim-Kwang Raymond Choo

  3. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

    Saminathan Ponnusamy

  4. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  5. Department of Computer Engineering, Ondokuz Mayis University, Atakum, Turkey

    Sedat Akleylek

  6. Department of Information Technology, Indian Institute of Engineering Science and Technology, West Bengal, India

    Santi Prasad Maity

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Lobo, J.Z. (2022). Application of Group Methods in Solving Wave Equations. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_65

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