Exploring Nonlinear Elastic Wave Equations
Author Information
Author(s): Hussain Akhtar, Usman M., Zaman Fiazuddin, Zidan Ahmed M., Herrera Jorge
Primary Institution: Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
Hypothesis
This study aimed to explore the behavior of nonlinear elastic wave equations and their underlying physical properties using Lie group invariants.
Conclusion
The research provides unique analytical solutions and conservation laws for nonlinear elastic wave equations, highlighting the effectiveness of the Lie group method.
Supporting Evidence
- The study derived an eight-dimensional symmetry algebra for the (3+1)-dimensional nonlinear elastic wave equation.
- Group-invariant solutions were obtained using the optimal system derived from the Lie group method.
- Noether's theorem was applied to uncover conservation laws for the nonlinear elastic wave equations.
- The research highlights the application of variational calculus to the existing literature on elastic wave equations.
Takeaway
The study looks at how certain waves in materials behave and finds new ways to understand them using math.
Methodology
The Lie group method was used to analyze the nonlinear elastic wave equations and derive conservation laws.
Digital Object Identifier (DOI)
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