Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation
Type :
Article
Publication Status :
Published
Access :
restrictedAccess
Abstract
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.
Source :
Studies in Applied Mathematics
Date :
2022-07
Volume :
149
Issue :
1
Publisher :
Wiley
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