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CUMHURIYET SCIENCE JOURNAL, vol.46, no.3, pp.583-589, 2025 (TRDizin)
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.