Integrability, similarity reductions and solutions for a (3+1)-dimensional modified Kadomtsev–Petviashvili system with variable coefficients

Abstract

In this study, a (3+1)-dimensional modified Kadomtsev–Petviashvili system with variable-coefficients (vcmKP) arising in many fields of science like plasma physics, optics, and fluid mechanics is studied. The consistent Riccati expansion solvability technique is applied to the vcmKP system to obtain necessary integrability conditions between the variable coefficients. Moreover, many novel different types of travelling wave solutions are given. Additionally, the vcmKP system is reduced to a nonlinear third order ordinary differential equation and many other new solutions are obtained. Finally, some plots are given to illustrate how the arbitrary function choices affect the propagation of the wave solutions.

Keywords

• (3+1)-dimensional modified Kadomtsev–Petviashvili system with variable-coefficients
• Integrability technique
• Similarity reductions
• Solitary wave solutions
• Rational wave solutions
• Periodic wave solutions