Orbital stability of solitary wave solutions of a Hamiltonian PDE arising in magma dynamics

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We consider a Hamiltonian PDE arising from a class of equations appearing in the study of magma dynamics in the Earth’s interior. Previously, it has been shown that the Hamiltonian PDE admits solitary wave solutions. Simpson et al. proved that the solitary wave solutions are orbitally stable for the case n=2. We verify the stability criterion analytically for the case n=3. Our results answer partially an open question proposed by Simpson et al. (2008).