| Abstract: |
| Solitons offer fundamental insight into the dynamics of nonlinear systems and arise in a wide range of applications across physics and mathematics. The Hirota bilinear method provides a powerful framework for analyzing such solutions in integrable PDEs, enabling the systematic construction of multi-soliton solutions by transforming nonlinear PDEs into bilinear form. In this talk, we examine criteria for the existence of $N$-soliton solutions, illustrated through examples in both (1+1)- and (2+1)-dimensional settings. We also explore generalized bilinear equations and their corresponding soliton solutions. |
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