... 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. Findings The Painlevé analysis shows that the compatibility condition for integrability does not die away at the highest resonance level...

...Abdul-Majid Wazwaz Purpose This study aims to introduce a variety of integrable Boussinesq equations with distinct dimensions. Design/methodology/approach The author formally uses the simplified Hirota’s method and lump schemes for exploring lump solutions, which are rationally localized...

.../methodology/approach This formally uses 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. Findings This paper confirms the complete integrability of the newly developed (3 + 1...

...Abdul-Majid Wazwaz Purpose This study aims to develop two integrable shallow water wave equations, of higher-dimensions, and with constant and time-dependent coefficients, respectively. The author derives multiple soliton solutions and a class of lump solutions which are rationally localized...

...Jin-Jin Mao; Shou-Fu Tian; Xing-Jie Yan; Tian-Tian Zhang Purpose The purpose of this study is to examine the lump solutions of the (3 + 1)-dimensional nonlinear evolution equations by considering a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and a (3 + 1)-dimensional...

... polynomials. Design/methodology/approach Based on the bilinear form of new reduced form of the (3 + 1)-dimensional generalized BKP equation, lump solutions with sufficient and necessary conditions to guarantee analyticity and rational localization of the solutions are discovered. Also, extended homoclinic...