Borluk, HandanBruell, G.Nilsson, D.2023-06-212023-06-212022-070022-2526http://hdl.handle.net/10679/8451https://doi.org/10.1111/sapm.12494Of 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.engrestrictedAccessarticle14919512300077208370000110.1111/sapm.12494Dimension-breaking bifurcationExponential time differencingFractional Kadomtsev–Petviashvili equationPetviashvili iterationSolitary wavesTransverse instability2-s2.0-85126886841