Wave propagation through a 2D lattice (Q1573927)

The authors study the wave propagation through a 2D lattice for three special cases -- quadratic nonlinearity, cubic nonlinearity and both of these together. In each concrete case, the equation of motion reduces to a different nonlinear equation. For a quadratic nonlinearity the authors obtain the well-known Kadomtsev-Petviashvili (KP) equation and for a cubic nonlinearity the modified KP equation. When both of them are applied they derive an integro-differential equation. Moreover, the authors investigate the integrability of these equations using singularity analysis and obtain solitary wave equations.