Abstract
We consider the Cauchy problem of the Ostrovsky–Vakhnenko (OV) equation expressed in the new variables (y,τ)q3−q(logq)yτ−1=0 with Schwartz initial data q0(y)>0 which supports smooth and single-valued solitons. It is shown that the solution to the Cauchy problem for the OV equation can be characterized by a 3 × 3 matrix Riemann–Hilbert (RH) problem. Furthermore, by employing the ∂̄-steepest descent method to deform the RH problem into solvable models, we derive the soliton resolution for the OV equation across two space–time regions: y/τ>0 and y/τ<0. This result also implies that the N-soliton solutions of the OV equation in variables (y,τ) are asymptotically stable.
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