Scaling and hetero-/auto-Bäcklund transformations with solitons of an extended coupled (2+1)-dimensional Burgers system for the wave processes in hydrodynamics and acoustics

Abstract

The Burgers-type equations are applied to oceanography, hydrodynamic turbulence, gas dynamics, shock-wave formation, acoustic transmission structure, boundary-layer behavior, continuum-traffic simulation, convection-dominated diffusion, wave formation in the thermo-elastic media, vorticity transport, dispersion in the porous media, particle sedimentation in fluid suspension, colloid evolution, and so forth. Hereby, taking into account the wave processes in hydrodynamics and acoustics, we investigate an extended coupled (2+1)-dimensional Burgers system, and with symbolic computation, work out a scaling transformation, two hetero-Bäcklund transformations and two auto-Bäcklund transformations, with the soliton solutions. Our results are dependent on the coefficients in the system.