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- Title
An Invariance and Closed Form Analysis of the Nonlinear Biharmonic Beam Equation.
- Authors
Masood, Y.; Kara, A. H.; Zaman, F. D.
- Abstract
In this paper, we study the one-parameter Lie groups of point transformations that leave invariant the biharmonic partial differential equation (PDE) uxxxx + 2uxxyy + uyyyy = f(u). To this end, we construct the Lie and Noether symmetry generators and present reductions of biharmonic PDE. When f is arbitrary function of u, we obtain the solution of biharmonic equation in terms of Green function. The equation is further analysed when f is exponential function and for general power law. Furthermore, we use Noether's theorem and the 'multiplier approach' to construct conservation laws of the PDE.
- Subjects
TRANSFORMATION groups; NOETHER'S theorem; PARTIAL differential equations; NONLINEAR analysis; CONSERVATION laws (Physics); BIHARMONIC equations; CONSERVATION laws (Mathematics)
- Publication
Malaysian Journal of Mathematical Sciences, 2023, Vol 17, Issue 2, p211
- ISSN
1823-8343
- Publication type
Article
- DOI
10.47836/mjms.17.2.09