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Volume 5, Issue 4
Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation

Ben Yang, Yunjia Song, Yanzhi Ma & Xinxue Zhang

DOI: 10.12150/jnma.2023.708

J. Nonl. Mod. Anal., 5 (2023), pp. 708-719.

Published online: 2023-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers.

  • Keywords

One-dimensional nonlinear wave equation, Lie symmetry, optimal system, conservation law.

  • AMS Subject Headings

35A08, 35C08, 35Q51

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-708, author = {Yang , BenSong , YunjiaMa , Yanzhi and Zhang , Xinxue}, title = {Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {4}, pages = {708--719}, abstract = {

Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.708}, url = {http://global-sci.org/intro/article_detail/jnma/22203.html} }
TY - JOUR T1 - Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation AU - Yang , Ben AU - Song , Yunjia AU - Ma , Yanzhi AU - Zhang , Xinxue JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 708 EP - 719 PY - 2023 DA - 2023/12 SN - 5 DO - http://doi.org/10.12150/jnma.2023.708 UR - https://global-sci.org/intro/article_detail/jnma/22203.html KW - One-dimensional nonlinear wave equation, Lie symmetry, optimal system, conservation law. AB -

Based on classical Lie symmetry method, the one-dimensional nonlinear wave equation is investigated. By using four-dimensional subalgebras of the equation, the invariant groups and commutator table are constructed. Furthermore, optimal system of the equation is obtained, and the exact solutions can be gained by solving reduced equations. Finally, a complete derivation of the conservation law is given by using conservation multipliers.

Ben Yang, Yunjia Song, Yanzhi Ma & Xinxue Zhang. (2023). Group-Invariant Solutions and Conservation Laws of One-Dimensional Nonlinear Wave Equation. Journal of Nonlinear Modeling and Analysis. 5 (4). 708-719. doi:10.12150/jnma.2023.708
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