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

Abstract

Purpose

This study aims to investigate two newly developed (3 + 1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects.

Design/methodology/approach

The Painlevé analysis confirms the complete integrability of both Kairat-II and Kairat-X equations.

Findings

This study explores multiple soliton solutions for the two examined models. Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.

Research limitations/implications

The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.

Practical implications

This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. In addition, lump solutions and breather wave solutions were achieved from Kairat-X model.

Social implications

The work formally furnishes algorithms for studying newly constructed systems that examine plasma physics, optical communications, oceans and seas and the differential geometry of curves, among others.

Originality/value

This paper presents an original work that presents two newly developed Painlev\'{e} integrable models with insightful findings.

Citation

Wazwaz, A.-M. (2024), "Extended (3 + 1)-dimensional Kairat-II and Kairat-X equations: Painlevé integrability, multiple soliton solutions, lump solutions, and breather wave solutions", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/HFF-01-2024-0053