Abstract
•We construct conservation laws using the results of Anco & Bluman and proceed to determine conserved densities.•This is the first time conservation law constructions are done for oscillon solution systems.•We study coupled scalar fields and two one-dimensional spatial vector oscillons.
In this paper, we construct and analyse the conservation laws (conserved densities) of two models that lead to oscillons; viz., in a system of two nonlinearly coupled scalar fields in (1+1)-dimensional spatiotemporal continuum and analysed a particular class of sixth-degree polynomial potentials and one in which an interaction of ‘two one-dimensional spatial vector oscillons in a trap with significant transverse dimensions’ occurs.