Variational Analysis and Integration of the (2 + 1) Fourth-Order Time-Dependent Biharmonic Equation via Energy and Momentum Conservation
We consider the fourth-order PDE uxxxx+2uxxyy+uyyyy−utt=h(u). The Lie and Noether symmetry generators are constructed, and we reduce the PDE to simpler ODEs. Furthermore, we use some well-known methods to compute the conserved vectors associated with the PDE. An analysis of reduced ordinary differential equations (ODEs), invariant solutions, and their physical interpretations is presented.
Authors
- A. H. Kara (ORCID: https://orcid.org/0000-0002-0231-0198)
- F. D. Zaman (ORCID: https://orcid.org/0000-0002-6498-0664)
- Yasir Masood
- Ali Raza (ORCID: https://orcid.org/0000-0002-7593-9923)
Institutions
- University of the Witwatersrand (ZA)
- Stellenbosch University (ZA)
- National Institute for Theoretical Physics (ZA)
- Government College University, Lahore (PK)
Publication Details
- Journal
- Symmetry
- Published
- 2025-11-03
- DOI
- https://doi.org/10.3390/sym17111845
- Primary Topic
- Nonlinear Waves and Solitons
- Type
- article
- Field-Weighted Citation Impact
- 0.00