| Abstract: |
| Higher-order nonlinear wave models have recently attracted significant interest from researchers due to their importance in mathematical physics, various nonlinear sciences, and engineering applications. In this talk, we present analytical studies focused on a generalized form of a nonlinear breaking soliton equation with higher-order nonlinearity, highlighting its relevance to both science and engineering. We employ Lie group theory and derive a Lie algebra associated with the equation. This approach also facilitates reductions of various subalgebras related to the model. Additionally, we use direct integration techniques to obtain an analytic solution. Furthermore, we apply the simplest equation technique to uncover additional general solutions. Finally, we compute the conserved quantities associated with the equation using the well-known Noether theorem. |
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