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The addition of higher order asymptotic corrections to the Korteweg-de Vries equation results in the extended Korteweg-de Vries (eKdV) equation. These higher order terms destabilize the dispersive shock wave solution, also termed an undular bore in fluid dynamics, and result in the emission of resonant radiation. In broad terms, there are three possible dispersive shock wave regimes: radiating dispersive shock wave (RDSW), cross-over dispersive shock wave (CDSW) and travelling dispersive shock wave (TDSW). While there are existing solutions for the RDSW and TDSW regimes obtained using modulati...

Abstract In this work, the dispersive shock wave (DSW) solution of a Boussinesq Benjamin–Ono (BBO) equation, the standard Boussinesq equation with dispersion replaced by nonlocal Benjamin–Ono dispersion, is derived. This DSW solution is derived using two methods, DSW fitting and from a simple wave solution of the Whitham modulation equations for the BBO equation. The first of these yields the two edges of the DSW, while the second yields the complete DSW solution. As the Whitham modulation equations could not be set in Riemann invariant form, the ordinary differential equations governing ...