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Modulated equations of Hamiltonian PDEs and dispersive shocks. (English) Zbl 1457.35052

Periodic traveling waves of Hamiltonian PDE (such as KdV and Euler-Korteweg) are considered in the limits of small amplitude and large wavelength. Then, the asymptotics of associated modulation systems is thoroughly studied in the soliton and in the harmonic limits.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
35C07 Traveling wave solutions
35C08 Soliton solutions
35B10 Periodic solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
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