Painleve analysis, Backlund transformations and traveling-wave solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid

Fluids are seen in such disciplines as atmospheric science, oceanography and astrophysics. In this paper, we investigate a (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid. On the basis of the Painleve analysis, we find that the equation is Painleve integrable under a certain constraint. Through the truncated Painleve expansion, we give an auto-Backlund transformation. By virtue of the Hirota method, we derive a bilinear auto-Backlund transformation. Via the polynomial-expansion method, traveling-wave solutions are obtained. We observe that the amplitude of a traveling wave remains invariant during the propagation. We graphically demonstrate that the amplitude of the traveling-wave is affected by the coefficients corresponding to the dispersion and nonlinearity effects, while other coefficients have no influence on the traveling-wave amplitude, which represent the perturbed effects and disturbed wave velocity effects.

Automated summary

In this paper, a (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid is investigated, showing the equation is Painleve integrable under certain constraint. An auto-Backlund transformation and a bilinear auto-Backlund transformation are derived through Painleve analysis and Hirota method, respectively. By using the polynomial-expansion method, traveling-wave solutions are obtained, with the amplitude of the wave remaining invariant during propagation. The amplitude of the traveling wave is found to be influenced by coefficients corresponding to dispersion and nonlinearity effects, while other coefficients have no impact on the wave amplitude.