Two new integrable Kadomtsev–Petviashvili equations with time-dependent coefficients: multiple real and complex soliton solutions

ABSTRACT

In this work, we develop two new integrable Kadomtsev–Petviashvili (KP) equations with time-dependent coefficients. The integrability property of each equation is explicitly demonstrated exhibiting the Painlevé test to confirm its integrability. Moreover, each equation admits multiple real and multiple complex soliton solutions. We introduce complex forms of the simplified Hirota's method to derive multiple complex soliton solutions. These two model equations are likely to be of applicative relevance, because it may be considered an application of a large class of nonlinear KP equations.

KEYWORDS:

• KP equation
• simplified Hirota's method
• complex forms
• multiple complex soliton solutions

Disclosure statement

No potential conflict of interest was reported by the authors.