Extended (3 + 1)-dimensional Kairat-II and Kairat-X equations: Painlevé integrability, multiple soliton solutions, lump solutions, and breather wave solutions

What is it about?

This study investigates two newly developed (3+1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects. The paper presents an original work that presents two newly developed Painlev\'{e} integrable models with insightful findings.

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