Traveling waves and transverse instability for the fractional Kadomtsev-Petviashvili equation. (English) Zbl 1529.35119
Summary: Of concern are traveling wave solutions for the fractional Kadomtsev-Petviashvili (fKP) equation. The existence of periodically modulated solitary wave solutions is proved by dimension-breaking bifurcation. Moreover, the line solitary wave solutions and their transverse (in)stability are discussed. Analogous to the classical Kadmomtsev-Petviashvili (KP) equation, the fKP equation comes in two versions: fKP-I and fKP-II. We show that the line solitary waves of fKP-I equation are transversely linearly instable. We also perform numerical experiments to observe the (in)stability dynamics of line solitary waves for both fKP-I and fKP-II equations.
{© 2022 Wiley Periodicals LLC.}
{© 2022 Wiley Periodicals LLC.}
MSC:
| 35C07 | Traveling wave solutions |
| 35C08 | Soliton solutions |
| 35B32 | Bifurcations in context of PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
dimension-breaking bifurcation; exponential time differencing; fractional Kadomtsev-Petviashvili equation; Petviashvili iteration; solitary waves; transverse instabilityReferences:
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