Title: Normal form for transverse instability of the line soliton with a nearly critical speed of propagation,
Abstract: There exists a critical speed of propagation of the line solitons in the
Zakharov-Kuznetsov (ZK) equation such that small transversely periodic
perturbations are unstable for line solitons with larger-than-critical speeds
and orbitally stable for those with smaller-than-critical speeds. The normal
form for transverse instability of the line soliton with a nearly critical
speed of propagation is derived by means of symplectic projections and
near-identity transformations. Justification of this normal form is provided
with the energy method. The normal form predicts a transformation of the
unstable line solitons with larger-than-critical speeds to the orbitally stable
transversely modulated solitary waves.