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 in all directions in space.
Design/methodology/approach
The author uses the simplified Hirota’s method and lump technique for determining multiple soliton solutions and lump solutions as well. The author shows that the developed (2+1)- and (3+1)-dimensional models are completely integrable in in the Painlené sense.
Findings
The paper reports new Painlevé-integrable extended equations which belong to the shallow water wave medium.
Research limitations/implications
The author addresses the integrability features of this model via using the Painlevé analysis. The author reports multiple soliton solutions for this equation by using the simplified Hirota’s method.
Practical implications
The obtained lump solutions include free parameters; some parameters are related to the translation invariance and the other parameters satisfy a non-zero determinant condition.
Social implications
The work presents useful algorithms for constructing new integrable equations and for the determination of lump solutions.
Originality/value
The paper presents an original work with newly developed integrable equations and shows useful findings of solitary waves and lump solutions.
New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients