Reduction Operators of Linear Second-Order Parabolic Equations

Details Reduction Operators of Linear Second-Order Parabolic Equations Reduction Operators of Linear Second-Order Parabolic Equations

2007-12-17

arxiv.org/abs/0712.2764v3

J. Phys. A: Math. Theor., 2008, V. 41, 185202, 31 pp

Mathematics

Analysis of PDEs

31 pages, minor misprints are corrected

Scientific paper

10.1088/1751-8113/41/18/185202

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary differential ones are exhaustively described. This problem proves to be equivalent, in some sense, to solving the initial equations. The ``no-go'' result is extended to the investigation of point transformations (admissible transformations, equivalence transformations, Lie symmetries) and Lie reductions of the determining equations for the nonclassical symmetries. Transformations linearizing the determining equations are obtained in the general case and under different additional constraints. A nontrivial example illustrating applications of reduction operators to finding exact solutions of equations from the class under consideration is presented. An observed connection between reduction operators and Darboux transformations is discussed.

Affiliated with

Also associated with

No associations

Rating

Reduction Operators of Linear Second-Order Parabolic Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reduction Operators of Linear Second-Order Parabolic Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reduction Operators of Linear Second-Order Parabolic Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-116605