Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations - art. no. 026608

Solitons play a fundamental role in the evolution of general initial data f or quasilinear dispersive partial differential equations, such as the Korte weg-de Vries (KdV), nonlinear Schrodinger, and the Kadomtsev-Petviashvili e quations. These integrable equations have linear dispersion and the soliton s have infinite support. We have derived and investigate a new KdV-like Ham iltonian partial differential equation from a four-parameter Lagrangian whe re the nonlinear dispersion gives rise to solitons with com pact support (c ompactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integra ble partial differential equations. The compactons formed from arbitrary in itial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapp licability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying t he processes beyond integrability. We have found explicit formulas for mult iple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compac ton is the minimum of a reduced Hamiltonian and is the only one that is sta ble.