New Solitary Wave Solutions in nonlinear physics using an extended rational exponential approach

an extended rational exponential approach

Résumé

This study introduces an innovative analytical approach to derive exact solitary wave solutions for nonlinear fractional order equations. By employing the extended rational exp-expansion method, we obtain novel solitary wave solutions for two prominent nonlinear physical models: the Maccari system and the Higgs equation. The method is demonstrated to effectively solve fractional order nonlinear partial differential equations, yielding previously unreported solitary wave configurations including kink, singular-kink, and periodic wave solutions. The physical relevance of these results are rigorously analyzed and supported by their graphical illustrations. A comparative study indorses the enhanced reliability and computational efficiency of the proposed method.  The study introduces an innovative analytical approach to derive exact solitary wave solutions. These results also highlight the adaptability of this method, which has considerable significance for solving a wide range of nonlinear evolution equations that arise in mathematical physics and engineering applications.