Abstract
PurposeThis paper aims to propose a new (3+1)-dimensional integrable Hirota bilinear equation characterized by five linear partial derivatives and three nonlinear partial derivatives. Design/methodology/approachThe authors formally use the simplified Hirota's method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space. FindingsThe Painleve analysis shows that the compatibility condition for integrability does not die away at the highest resonance level, but integrability characteristics is justified through the Lax sense. Research limitations/implicationsMultiple-soliton solutions are explored using the Hirota's bilinear method. The authors also furnish a class of lump solutions using distinct values of the parameters via the positive quadratic function method. Practical implicationsThe authors also retrieve a bunch of other solutions of distinct structures such as solitonic, periodic solutions and ratio of trigonometric functions solutions. Social implicationsThis work formally furnishes algorithms for extending integrable equations and for the determination of lump solutions. Originality/valueTo the best of the authors' knowledge, this paper introduces an original work with newly developed Lax-integrable equation and shows new useful findings.