Kink-soliton, singular-kink-soliton and singular-periodic solutions for a new two-mode version of the Burger–Huxley model: applications in nerve fibers and liquid crystals

New two-mode version of the generalized Burger–Huxley equation is derived using Korsunsky’s operators. The new model arises in applications nerve fibers and liquid crystals, it describes interaction two symmetric waves moving simultaneously same direction. Solitary wave solutions types kink-soliton, singular-kink-soliton singular-periodic are obtained to this by means simplified bilinear method, polynomial-function method Kudryashov-expansion method. A comprehensive graphical analysis conducted show some physical properties type nonlinear equations. Finally, all verified direct substitutions model.