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Purpose
This study aims to extend Painlevé integrable (3 + 1)-dimensional Estevez– Prada equation.
Design/methodology/approach
The Painlevé integrability of this equation will be tested via Mathematica program.
Findings
This study explores multiple soliton solutions for the examined integrable model.
Research limitations/implications
The Hirota’s bilinear algorithm is used to derive multiple soliton solutions.
Practical implications
The author also furnishes a variety of distinct structures, such as kink, periodic, singular and rational, as well.
Social implications
The work presents useful algorithms for investigating new integrable systems.
Originality/value
The paper presents an original work that presents two newly developed Painlevé integrable models with insightful findings.
© Emerald Publishing Limited
2025
Emerald Publishing Limited
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