Study on a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation in nonlinear physics: Multiple soliton solutions, lump solutions, and breather wave solutions

In this work, we study an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equations that appear in many nonlinear physics applications. We show that this extended equation retains its complete integrability via Painlevé analysis. We explore multiple soliton solutions by using the Hirota bilinear method. Moreover, we derive lump solutions where two numerical examples are tested. Breather wave solutions were also explored by using a variety of distinct schemes. We also determine other traveling wave solutions, rational solutions, periodic solutions, exponential solutions, ratio of trigonometric or hyperbolic functions, and others. • We study an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation. • We explore multiple soliton solutions by using the Hirota bilinear method. • We derive lump solutions and breather wave solutions.