Lie Symmetry Analysis of Burgers Equation and the Euler Equation on a Time Scale

As a powerful tool that can be used to solve both continuous and discrete equations, the Lie symmetry analysis of dynamical systems on a time scale is investigated. Applying the method to the Burgers equation and Euler equation, we get the symmetry of the equation and single parameter groups on a time scale. Some group invariant solutions in explicit form for the traffic flow model simulated by a Burgers equation and Euler equation with a Coriolis force on a time scale are studied.

[1]  Dumitru Baleanu,et al.  Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation , 2018, Commun. Nonlinear Sci. Numer. Simul..

[2]  C. Chyan.  Uniqueness Implies Existence on Time Scales , 2001 .

[3]  Aubrey Truman,et al.  The stochastic Burgers equation with vorticity: Semiclassical asymptotic series solutions with applications , 2011 .

[4]  Allan C. Peterson,et al.  Boundedness and Uniqueness of Solutions to Dynamic Equations on Time Scales , 2003 .

[5]  Huaiping Zhu,et al.  Existence and roughness of exponential dichotomies of linear dynamic equations on time scales , 2010, Comput. Math. Appl..

[6]  Jia Man,et al.  Relation between the Induced Flow and the Position of Typhoon: Chanchu 2006 , 2006 .

[7]  Haibo Chen,et al.  Double positive solutions of boundary value problems for p-Laplacian impulsive functional dynamic equations on time scales , 2007, Comput. Math. Appl..

[8]  S. Lou,et al.  Symmetry analysis and exact solutions of the 2+1 dimensional sine-Gordon system , 2000 .

[9]  S. Hilger.  Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[10]  Márcia Federson,et al.  Boundedness of solutions of measure differential equations and dynamic equations on time scales , 2017 .

[11]  Hanze Liu,et al.  Symmetry reductions, dynamical behavior and exact explicit solutions to the Gordon types of equations , 2014, J. Comput. Appl. Math..

[12]  Pablo Amster,et al.  Existence of solutions to boundary value problems for dynamic systems on time scales , 2005 .

[13]  Christopher C. Tisdell,et al.  Stability and instability for dynamic equations on time scales , 2005 .

[14]  Jan Nordström,et al.  Numerical analysis of the Burgers' equation in the presence of uncertainty , 2009, J. Comput. Phys..

[15]  Wan-Tong Li,et al.  Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales , 2007 .

[16]  W. Woyczynski,et al.  Fractal Burgers Equations , 1998 .

[17]  Ravi P. Agarwal,et al.  Triple solutions to boundary value problems on time scales , 2000, Appl. Math. Lett..

[18]  Yixiang Geng,et al.  Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid , 2013 .

[19]  Youngwoo Koh,et al.  Strichartz estimates for the Euler equations in the rotational framework , 2014 .

[20]  Stefan Heinz,et al.  Comments on a priori and a posteriori evaluations of sub-grid scale models for the Burgers’ equation , 2016 .

[21]  M. Lakshmanan,et al.  Lie point symmetries classification of the mixed Liénard-type equation , 2015 .