The stability of finite-amplitude interfacial solitary waves

The linear stability of finite-amplitude interfacial gravity solitary waves propagating in a two-layer fluid is investigated analytically focusing on the occurrence of an exchange of stability. We make an asymptotic analysis for small growth rates of infinitesimal disturbances, and explicitly obtain their growth rates near an exchange of stability. The result indicates that an exchange of stability occurs at every stationary value of the total energy of the solitary waves. It also gives us information whether the number of growing modes increases or decreases after experiencing the exchange of stability. We apply these analytical results to specific interfacial solitary waves, and find various features on their stability that are not seen in the case of surface solitary waves.