Solitons, travelling waves, invariance, conservation laws and ‘approximate’ conservation of the extended Jimbo-Miwa equation

Abstract 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.