Hidden symmetries and exact solutions of integro-differential Jaulent-Miodek evolution equation

•Use of the adjoint method, to obtain optimal Lie vectors.•A reduction of the JM equation to ordinary differential equations and detection of Lie symmetries.•Test if these symmetries are hidden.•Analysis and plot of results.•Comparison with previous work in the field.

Analytical solutions of a '(2 + 1)' dimensional nonlinear model using the Jaulent-Miodek hierarchy are investigated following a similarity reduction procedure. For this adjoint Lie matrices are first evaluated and an extensive list of optimal Lie vectors is obtained. The systematic reduction of Jaulent-Miodek evolution equation to lower number of variables leads to hidden symmetries and new solutions.