Geodesic
Hugoniót--Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations
Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 902-913

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For the “phase” of vortex singular solutions of the shallow water equations we justify the Hamilton–Jacobi equation corresponding to the hydrodynamical mode of perturbation propagation. We also obtain the next correction to the Cauchy–Riemann conditions describing how the singular part of the solution affects the smooth background. 
@article{MZM_2002_71_6_a9,
     author = {E. S. Semenov},
     title = {Hugoni\'ot--Maslov {Conditions} for {Vortex} {Singular} {Solutions} of the {Shallow} {Water} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {902--913},
     publisher = {mathdoc},
     volume = {71},
     number = {6},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a9/}
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E. S. Semenov. Hugoniót--Maslov Conditions for Vortex Singular Solutions of the Shallow Water Equations. Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 902-913. http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a9/