Reduction operators of Burgers equation
Copyright policy )Reduction operators of Burgers equation
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
11 pages, minor corrections
- Universität Wien Austria
- University of Vienna Austria
- Institute of Mathematics NAS of Ukraine Ukraine
- MEDIZINISCHE UNIVERSITAT GRAZ Austria
- Universität Wien Austria
exact solution, FOS: Physical sciences, PDEs in connection with fluid mechanics, Methods of ordinary differential equations applied to PDEs, Article, Mathematics - Analysis of PDEs, reduction operator, FOS: Mathematics, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Exact solution, Applied Mathematics, Mathematical Physics (math-ph), Burgers equation, 35A30 (Primary) 35C05, 35K59, 35K05 (Secondary), Lie symmetry, nonclassical symmetry, Reduction operator, Explicit solutions, first integrals of ordinary differential equations, Nonclassical symmetry, Exactly Solvable and Integrable Systems (nlin.SI), Analysis, Analysis of PDEs (math.AP)
exact solution, FOS: Physical sciences, PDEs in connection with fluid mechanics, Methods of ordinary differential equations applied to PDEs, Article, Mathematics - Analysis of PDEs, reduction operator, FOS: Mathematics, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Exact solution, Applied Mathematics, Mathematical Physics (math-ph), Burgers equation, 35A30 (Primary) 35C05, 35K59, 35K05 (Secondary), Lie symmetry, nonclassical symmetry, Reduction operator, Explicit solutions, first integrals of ordinary differential equations, Nonclassical symmetry, Exactly Solvable and Integrable Systems (nlin.SI), Analysis, Analysis of PDEs (math.AP)
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