Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-f...Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-fold Darboux transformation(DT) and conservation laws for the lattice Burgers equation are constructed based on its Lax pair.N-soliton solutions in the form of Vandermonde-like determinant are derived via the resulting DT with symbolic computation,structures of which are shown graphically.Coexistence of the elastic-inelastic interaction among the three solitons is firstly reported for the lattice Burgers equation,even if the similar phenomenon for certern continuous systems is known.Results in this paper might be helpful for understanding some ecological problems describing the evolution of competing species and the propagation of nonlinear waves in fluids.展开更多
基金Supported by the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-2012ZX-10,Beijing University of Aeronautics and Astronauticsthe Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02+2 种基金the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications)the Specialized Research Fund for the Doctoral Program of Higher Education (No. 200800130006),Chinese Ministry of Educationthe Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No. KM201010772020
文摘Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-fold Darboux transformation(DT) and conservation laws for the lattice Burgers equation are constructed based on its Lax pair.N-soliton solutions in the form of Vandermonde-like determinant are derived via the resulting DT with symbolic computation,structures of which are shown graphically.Coexistence of the elastic-inelastic interaction among the three solitons is firstly reported for the lattice Burgers equation,even if the similar phenomenon for certern continuous systems is known.Results in this paper might be helpful for understanding some ecological problems describing the evolution of competing species and the propagation of nonlinear waves in fluids.
