Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics

Under investigation in this paper is a modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics. Painlevé integrability is investigated. Soliton-cnoidal and resonant solutions are derived via the consistent tanh expansion method. The equation is reduced to certain symmetry reduction equations via the Lie point symmetry generators obtained though the Lie group method. Hyperbolic function and rational solutions are derived through those symmetry reduction equations.