Painleve analysis, auto-Backlund transformation and analytic solutions of a (2+1)-dimensional generalized Burgers system with the variable coefficients in a fluid

Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a (2+1)-dimensional generalized Burgers system with the variable coefficients in a fluid is investigated. We obtain the Painleve-integrable constraints of the system with respect to the variable coefficients. Based on the truncated Painleve expansions, an auto-Backlund transformation is constructed, along with some soliton solutions. Via a truncated Painleve expansions, certain multiple kink solutions are derived. Via a complex-conjugate transformation, some breather solutions, half-periodic kink solutions and hybrid solutions composed of the breathers and kink waves are seen.

Automated summary

This paper investigates a (2+1)-dimensional generalized Burgers system with variable coefficients in a fluid. It obtains the Painleve-integrable constraints of the system with respect to the variable coefficients. Based on truncated Painleve expansions, an auto-Backlund transformation is constructed, along with soliton solutions. Multiple kink solutions are derived using truncated Painleve expansions. Breather solutions, half-periodic kink solutions, and hybrid solutions composed of breathers and kink waves are obtained via complex-conjugate transformation.