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Article Dans Une Revue Letters in Mathematical Physics Année : 2021

Numerical study of break-up in solutions to the dispersionless Kadomtsev–Petviashvili equation

Résumé

We present a numerical approach to study solutions to the dispersionless Kadomtsev-Petviashvili (dKP) equation on R x T. The dependence on the coordinate x is considered on the compactified real line, and the dependence on the coordinate y is assumed to be periodic. Critical behavior, the formation of a shock in the solutions, is of special interest. The latter permits the numerical study of Dubrovin's universality conjecture on the break-up of solutions to the Kadomtsev-Petviashvili equation. Examples from a previous paper on dKP solutions studied numerically on T-2 are addressed, and the influence of the periodicity or not in the x-coordinate on the break-up is studied.
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Dates et versions

hal-03467044 , version 1 (06-12-2021)

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Christian Klein, Nikola Stoilov. Numerical study of break-up in solutions to the dispersionless Kadomtsev–Petviashvili equation. Letters in Mathematical Physics, 2021, 111 (5), ⟨10.1007/s11005-021-01454-6⟩. ⟨hal-03467044⟩
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