A study on a two-wave mode Kadomtsev-Petviashvili equation: conditions for multiple soliton solutions to exist

We establish a two-wave mode equation for the integrable Kadomtsev-Petviashvili equation, which describes the propagation of two different wave modes in the same direction simultaneously. We determine the necessary conditions that make multiple soliton solutions exist for this new equation. The simplified Hirota's method will be used to conduct this work. We also use other techniques to obtain other set of periodic and singular solutions for the two-mode Kadomtsev-Petviashvili equation. Copyright (c) 2017 John Wiley & Sons, Ltd.