Parametrix problem for the Korteweg-de Vries equation with steplike initial data. (English) Zbl 1528.35152
The KdV equation is considered with sufficiently smooth steplike initial data. In order to obtain precise asymptotics of solutions to the Cauchy problem, an approach based on the direct comparison of resolvents of the associated Riemann-Hilbert problem is applied. These solutions develop shock waves between asymptotically constant and soliton regions.
Reviewer: Piotr Biler (Wrocław)
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 76L05 | Shock waves and blast waves in fluid mechanics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 45E05 | Integral equations with kernels of Cauchy type |
Software:
DLMFReferences:
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