Abstract
PurposeThis study aims to explore novel solitary wave solutions of a new (3 + 1)-dimensional nonlocal Boussinesq equation that illustrates nonlinear water dynamics.Design/methodology/approachThe authors use the Painlevé analysis to study its complete integrability in the Painlevé sense.FindingsThe Painlevé analysis demonstrates the compatibility condition for the model integrability with the addition of new extra terms.Research limitations/implicationsThe phase shifts, phase variables and Hirota’s bilinear algorithm are used to furnish multiple soliton solutions.Practical implicationsThe authors also furnish a variety of numerous periodic solutions, kink solutions and singular solutions.Social implicationsThe work formally furnishes algorithms for investigating several physical systems, including plasma physics, optical communications and oceans and seas, among others.Originality/valueThis paper presents an original work using a newly developed Painlevé integrable model, as well as novel and insightful findings.
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