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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.

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