On the Derivation of Lax Pair Via Ablowitz-Kaup-Newell-Segur Formalism for Some Nonlinear Evolution Equations: A review | ||
| Benha Journal of Engineering Science and Technology | ||
| Volume 2, Issue 1, July 2025, Pages 145-153 PDF (393.18 K) | ||
| Document Type: Review Article | ||
| DOI: 10.21608/bjest.2025.446391 | ||
| Author | ||
| Mahmoud A. Khattab | ||
| Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, Egypt | ||
| Abstract | ||
| Extracting novel solutions to nonlinear evolution equations (NLEE's) is the ultimate goal of most analytical methods including inverse scattering transformations, Darboux transformations and Backlund transformations. These methods are mainly based on deriving the Lax pair for NLEE's, which is a pair of linear equations associated with the NLEE. In this paper, based on Ablowitz-Kaup-Newell-Segur (AKNS) formalism, we derive Lax pair for some NLEE's that appear in many engineering applications. This formalism ensures the derivation of Lax pair for many NLEE's with higher-order and higher dimensions. | ||
| Keywords | ||
| Lax Pair; AKNS formalism; Nonlinear evolution equations; soliton solutions | ||
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