The Derivation of a Fifth-Order Equation via the Lax and the Alternate Lax Methods
CUMHURIYET SCIENCE JOURNAL, cilt.46, sa.3, ss.583-589, 2025 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 46 Sayı: 3
- Basım Tarihi: 2025
- Doi Numarası: 10.17776/csj.1733907
- Dergi Adı: CUMHURIYET SCIENCE JOURNAL
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.583-589
- Recep Tayyip Erdoğan Üniversitesi Adresli: Evet
Özet
We present the derivation of a fifth-order integrable nonlinear partial differential equation via the Lax method and the alternate Lax method in the continuous case. The Lax method uses a pair of differential operators, 𝐿 and 𝐴, satisfying a compatibility condition. The pair (𝐿,𝐴) is known as the Lax pair. The alternate Lax method is a variation of the Lax method and use a consistency relation equivalent to the commutation of a certain derivative operator associated with the time evolution and the spacial evolution. In the paper we also show that the Lax method and the alternate Lax method are equivalent.