Generalized Camassa–Holm Equations: Symmetry, Conservation Laws and Regular Pulse and Front Solutions

In this paper, we consider a member of an integrable family generalized Camassa–Holm (GCH) equations. We make analysis the point Lie symmetries these equations by using method infinitesimals. derive nonclassical and find new via method, which cannot be obtained symmetry method. employ multiplier to construct conservation laws for GCH Using underlying equation, double reduction is also constructed. Finally, investigate traveling waves convergent series solutions both homoclinic heteroclinic orbits traveling-wave equations, correspond pulse front original respectively.