ANALYTICAL STUDY OF THE FAMILY OF M-FRACTIONAL 3-D WAZWAZ-BENJAMIN-BONA-MAHONY EQUATIONS

Abstract

Bu çalışma, kesikli (truncated) M-kesirli türev kullanılarak ve Geliştirilmiş Modifiye Sub-Denklem Yöntemi (Improved Modified Sub-Equation Method - IMSSEM) aracılığıyla üç tür üç boyutlu Wazwaz–Benjamin–Bona–Mahony (WBBM) denklemi için yeni soliton çözümleri türetmektedir. Hiperbolik, trigonometrik, rasyonel ve üstel biçimlerde çeşitli tam çözümler elde edilmiştir. Sonuçlar, IMSSEM yönteminin doğrusal olmayan evrim denklemlerinin çözümündeki etkinliğini ortaya koymakta ve rogue, kink, dark ve breather dalgalar gibi farklı dalga yapılarının incelenmesine olanak sağlamaktadır. Genel olarak önerilen yöntem, uygulamalı matematik, fizik ve mühendislik alanlarında ortaya çıkan doğrusal olmayan dalga dinamiklerinin araştırılmasında güçlü bir analitik araç olduğunu göstermektedir.

Keywords

• truncated M-fractional derivative
• dark wave.
• : WBBM equations
• IMSSEM
• breather wave

Analytical Study of the Family of M-Fractional 3-D Wazwaz-Benjamin-Bona-Mahony equations

Abstract

This study derives new soliton solutions for three types of three-dimensional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations using the Improved Modified Sardar Sub-Equation Method (IMSSEM) with the truncated M-fractional derivative. Various exact solutions in hyperbolic, trigonometric, rational, and exponential forms are obtained. The results highlight the effectiveness of IMSSEM in handling nonlinear evolution equations and uncover diverse wave structures, including rogue, breather, kink, dark, and bright waves. Overall, the proposed method proves to be a powerful analytical tool for studying nonlinear wave dynamics in physics and engineering applications.

Keywords

• WBBM equations
• IMSSEM
• truncated M-fractional derivative
• breather wave
• dark wave

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