Symmetries, travelling-wave and self-similar solutions of two-component BKP hierarchy

We investigate the two-component BKP hierarchy equation for its Lie point symmetries. To obtain a complete classification of the group-invariant solution, we derive the one-dimensional optimal system of subalgebras of A 3 , 3 ( D ⨂ s T 2 ) . By employing those subalgebras, we construct the invariant solutions which are represented through Weierstrass elliptic functions, Jacobi elliptic functions, and soliton solutions. Also, we analyse the existence of a bounded travelling-wave solution for the equation. Moreover, through the utilization of scale-invariant symmetry, we derive a self-similar solution. Additionally, by conducting singularity analysis, the solution can be expressed in the form of a right Painlevè series. • The two-component BKP hierarchy equation is studied under the lens of Lie symmetry. • We find the Lie point symmetries and perform a symmetry reduction of this equation. • Group invariant solutions are constructed.