Breather, lump, shock and travelling-wave solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics

Abstract

Investigation is conducted on a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics. By virtue of the homoclinic-test, ansatz and polynomial-expansion methods, we construct the breather and lump solutions, shock wave solutions and travelling-wave solutions, respectively. We observe that the breather propagates steadily along a straight line with certain angles with the x, y and z axes. We observe that the amplitude and shape of the bright-dark lump wave keep unchanged during the propagation. We observe that the amplitude and the shape of the shock wave keep unchanged during the propagation. We graphically analyse the effects of the coefficients in the equation on the breather, lump and shock waves. We find that the lump is the most stable while the shock wave is the least stable under the same perturbation among the breather, lump and shock waves.

Keywords:

• Fluid mechanics
• plasma physics
• (3+1)-dimensional generalized Kadomtsev–Petviashvili equation
• breather waves
• shock waves
• travelling waves

2010 Mathematics Subject Classifications:

• Generalized solutions to partial differential equations
• Partial differential equations of mathematical physics and other areas of application

Acknowledgments

This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the National Natural Science Foundation of China [grant numbers 11772017, 11272023 and 11471050], by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China [grant number 2011BUPTYB02].