MONOCHROMATIC WAVE PROPAGATION IN KP-TYPE EQUATION
KP-type equation is known as a wave equation with two spatial dimensions. The equation was derived in 1970 by Kadomtsev-Petviashvili. In this paper, we discuss the monochromatic wave propagation in KP-type equation that contains exact dispersion relation and nonlinearity in the x-direction. AB equation is taken as the nonlinear wave equation contained in that KP-type. The equation is revised version of the KdV equation for wave about finite depth and in certain approximation it becomes the KdV equation. The third order asymptotic method is applied for solving the KP-type equation by choosing monochromatic wave as a signal input. Comparison between the dispersion relation of KPAB and the other KP type is discussed to analyze the suitability of wave number of the KP. We also simulate the monochromatic wave propagation using the solution of the KP.
KP-type equation, AB-equation, third order asymptotic method, monochromatic wave.