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Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations

- Douglas Baldwin, Ünal Göktas, Willy Hereman
- Computer Physics Communications
- 2004

A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the… (More)

- Ünal Göktas, Willy Hereman
- J. Symb. Comput.
- 1997

and relies on the implicit function theorem. In contrast to our algorithm, their code makes no assumptions about the form of the conserved density. Further information can be obtained from Sanders at… (More)

- Douglas Baldwin, Ünal Göktas, Willy Hereman, Li Hong, R. S. Martino, J. C. Miller
- J. Symb. Comput.
- 2004

Algorithms are presented for the tanhand sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find… (More)

Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differential-difference equations are presented. The first algorithm is the well-known… (More)

- Ünal Göktas, Willy Hereman
- 1998

An algorithm to compute polynomial conserved densities of polynomial nonlinear lattices is presented. The algorithm is implemented in Mathematica and can be used as an automated integrability test.… (More)

- Ünal Göktas, Willy Hereman
- 1999

A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or… (More)

A new method for the computation of conserved densities of nonlinear differentialdifference equations is applied to Toda lattices and discretizations of the Korteweg-de Vries and nonlinear… (More)

- Ünal Göktas, Willy Hereman
- ArXiv
- 2010

An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite… (More)

- Ünal Göktas, Willy Hereman
- ArXiv
- 2010

Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations (DDEs) are… (More)

- Ünal Göktas, Willy Hereman
- Adv. Comput. Math.
- 1999