Rational Ansatz Research Articles

Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA

The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations. Program summaryProgram Title: CANONICAProgram Files doi:http://dx.doi.org/10.17632/fmwnmmhn77.1Licensing provisions: GNU General Public License version 3Programming language: Wolfram Mathematica, version 10 or higherNature of problem: Computation of a rational basis transformation of master integrals leading to a canonical form of the corresponding differential equation.Solution method: The transformation law is expanded in the dimensional regulator. The resulting differential equations for the expansion coefficients of the transformation are solved with a rational ansatz.

Multisoliton solutions to Hirota-Satsuma KdV system

In this paper, we obtain one and two soliton solutions to Hirota-Satsuma KdV system with the aid of tanh method and the multiple exp method. We also obtain some rational solutions by using a rational ansatz. The system Hirota-Satsuma KdV system is reduced to a single nonlinear partial differential equation which is solved by the described methods. Key words: Hirota-Satsuma KdV system, tanh method, multiple exp method one soliton solution, two soliton solution, HS coupled system.