Linear stability of weak-compacton solutions to the nonlinear dispersive Ostrovsky equation

Considered herein is the linear stability of compacton solutions to the nonlinear dispersive Ostrovsky equation, which is also a modification of the K(m,n)K(m,n) equation. We show that the equation does not pass the Painlevé test for integrability and has compacton solutions which are different from conventional forms. Furthermore, compactons are proved to be weak solutions. A new equation similar to the nonlinear dispersive Ostrovsky equation is derived from Lagrangian, and some important conservation laws as well as the Hamiltonian structure are given. Finally, the stability of the compacton solutions to the similar equations is studied via using linear stability analysis. The result shows that the linear stability analysis it follows that, unlike compactons to the K(m,n)K(m,n) equation, the weak-compacton solutions are linear stable under certain conditions.