Multi-Solitons, Multi-Breathers and Multi-Rational Solutions of Integrable Extensions of the Kadomtsev–Petviashvili Equation in Three Dimensions

The celebrated Korteweg–de Vries and Kadomtsev–Petviashvili (KP) equations are prototypical examples of integrable evolution in one two spatial dimensions, respectively. question constructing three-spatial dimensions has been the most important open problems history integrability. Here, we study an extension KP equation which can be derived using a specific reduction generalization four-spatial two-temporal (Phys. Rev. Lett. 96, (2006) 190201). For this new equation, construct smooth multi-solitons, high-order breathers, rational solutions, by Hirota’s bilinear method.