title: Dynamical systems theory for nonlinear evolution equations.
abstract: We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.
authors.affiliation: Department of Physics, Visva-Bharati, Santiniketan 731235, India.
authors.forename: Amitava
authors.initials: A
authors.lastname: Choudhuri
authors.forename: B
authors.initials: B
authors.lastname: Talukdar
authors.forename: Umapada
authors.initials: U
authors.lastname: Das