Two-dimensional instabilities of generalized Korteweg-de Vries waves

Instabilities of the generalized Korteweg-de Vries ((u_t+α₁u^mu_x+α₂uⁿu_x+u_xxx)_x+α₃u_yy = 0) waves wi th respect to two-dimensional infinitesimal longitudinal disturbances are investigated using the Infeld-Rowlands method. A linear dispersion relation expressed as a cubic equation in g̃w₁ is derived and instabilities of waves are discussed.