The Kadomtsev-Petviashvili equation in the neighborhood of a Morse critical point (Q1380299)

The paper revisits the derivation of the nonlinear complex multidimensional Klein-Gordon equation \[ u_{tt} - \nabla^2u - \delta_0 u =\delta_1 | u| ^2u, \] where \(\nabla^2\) is the two-dimensional Laplacian, \(\delta_0\) and \(\delta_1\) being real constants. In the paper, this equation is called ``Kadomtsev-Petviashvili equation'', although the latter name is usually reserved for equations of a very different form. The derivation is based on a generic expansion of the nonlinear dispersion relation for traveling waves in powers of small deviations of the frequency and wavenumbers, and small wave's intensity, in a vicinity of a point which is called ``Morse point'' in the paper (in a vicinity of the point, the first terms in the expansion in powers of the frequency and wavenumber deviations are quadratic).