Geodesic
Asymptotics of the Solutions of the One-Dimensional Nonlinear System of Equations of Shallow Water with Degenerate Velocity
Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 721-730

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A system of one-dimensional nonlinear equations of shallow water with degenerate velocity is considered. The change of variables taking the given system to a nonlinear system with small nonlinearity is proposed. Formal asymptotic solutions near the point of degeneracy are obtained.
Keywords: nonlinear system of equations of shallow water, Carrier–Greenspan transformation, Cauchy problem, Schwartz space, Duhamel integral, Hankel transform. 
@article{MZM_2012_92_5_a7,
     author = {D. S. Minenkov},
     title = {Asymptotics of the {Solutions} of the {One-Dimensional} {Nonlinear} {System} of {Equations} of {Shallow} {Water} with {Degenerate} {Velocity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {721--730},
     publisher = {mathdoc},
     volume = {92},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a7/}
}
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D. S. Minenkov. Asymptotics of the Solutions of the One-Dimensional Nonlinear System of Equations of Shallow Water with Degenerate Velocity. Matematičeskie zametki, Tome 92 (2012) no. 5, pp. 721-730. http://geodesic.mathdoc.fr/item/MZM_2012_92_5_a7/