The exact solutions of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si14.svg"><mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math>–dimensional Kadomtsev–Petviashvili equation with variable coefficients by extended generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg"><mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math>-expansion method

In this paper 2+1–dimensional Kadomtsev–Petviashvili (KP) equation with variable coefficients is investigated through the extended generalized G′G–expansion technique. One of the most universal model is KP equation, which is used to explain the ion acoustic waves in plasma physics, to model two dimensional shallow water waves, and in ferromagnetic, Bose–Einstein condensation and string theory. The obtained exact solutions of KP equation are in the form of hyperbolic function, trigonometric function, and rational function. With the aid of symbolic computational software Mathematica, the three dimensional surface plots with corresponding contour plots are provided for the obtained closed from solutions, which are of the form of solitary waves, multi solitons and periodic solitary wave like dynamical structures.