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New \((3+1)\)-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion

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Abstract

This work deals with a new \((3+1)\)-dimensional Painlevé integrable fifth-order equation characterized by third-order temporal and spatial dispersions. The Painlevé test is carried out to demonstrate the complete integrability of this model. A rule that governs the dispersion relation with the spatial variables coefficients is reported. We employ the simplified Hirota’s method to obtain multiple soliton solutions. We examine specific cases of the dispersion relations along with their respective coefficients. It is hoped that the results reported in this work can enrich applications in solitary waves theory, and more specifically, in models with third-order temporal dispersion.

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  1. Department of Mathematics, Saint Xavier University, Chicago, IL, 60655, USA

    Abdul-Majid Wazwaz

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Wazwaz, AM. New \((3+1)\)-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion. Nonlinear Dyn 106, 891–897 (2021). https://doi.org/10.1007/s11071-021-06872-8

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