This paper aims to investigate two integrable (2 + 1)-dimensional Kairat-II-X-extended and Kairat-II-X-type equations.
The two equations retain the Painlevé integrability.
This study investigates multifaceted solution structures for each model, encompassing multiple soliton configurations, lump wave phenomena and various forms of traveling wave solutions.
Hirota’s bilinear method is used to furnish these new solutions for each examined model.
This study further provides a diverse array of periodic solutions, kink solutions and singular solutions for the two integrable models.
This study systematically develops algorithms tailored for analyzing newly formulated systems across diverse domains.
This study introduces a novel contribution by developing new Painlevé integrable models with distinct structures and useful explorations.
