Continuous and Discrete Homotopy Operators with Applications in Integrability Testing

Details Continuous and Discrete Homotopy Operators with Applications in Integrability Testing Continuous and Discrete Homotopy Operators with Applications in Integrability Testing

2005-01-19

arxiv.org/abs/nlin/0501037v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D generalization allows one to invert the total divergence operator. As a practical application, we show how the operators can be used to symbolically compute local conservation laws of nonlinear systems of partial differential equations in multi-dimensions. By analogy to the continuous case, we also present concrete formulas for the discrete Euler and homotopy operators. Essentially, the discrete homotopy operator carries out summation by parts. We use it to algorithmically invert the forward difference operator. We apply the discrete operator to compute fluxes of differential-difference equations in (1+1) dimensions. Our calculus-based approach allows for a straightforward implementation of the operators in major computer algebra system, such as Mathematica and Maple. The symbolic algorithms for integration and summation by parts are illustrated with elementary examples. The algorithms to compute conservation laws are illustrated with nonlinear PDEs and their discretizations arising in fluid dynamics and mathematical physics.

Affiliated with

Also associated with

No associations

Rating

Continuous and Discrete Homotopy Operators with Applications in Integrability Testing 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 Continuous and Discrete Homotopy Operators with Applications in Integrability Testing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuous and Discrete Homotopy Operators with Applications in Integrability Testing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-641652