Abstract
•We construct symmetries and conservation laws of a class of Jimbo-Miwa equations.•Perform reductions of the equation.•Numerical presentations of the travelling wave solutions.
We will make a detailed analysis of a class of the Jimbo-Miwa equation, viz., exact or invariant solutions that arise from the symmetries generated by it and the conservation laws of the equation. The equation, it turns out, is rich in its symmetry structure and produces a large class of conservation laws and what we term as ‘approximate’ conservation laws.