CRACK swMATH ID: 7754 Software Authors: Wolf, Thomas Description: Applications of CRACK in the classification of integrable systems. The classifications of integrable systems are obtained by using a computer program. A method to reduce the length of the equations for large bilinear algebraic systems is presented. The integrable polynomial vector evolution equations, quadratic Hamiltonians with an e(3) Lie-Poisson structure and nonlocal 2+1-dimensional evolution equations are studied. An overview of the computer algebra program CRACK used in this paper is given and the algorithm designed to length-reduce differential equations is presented. The program CRACK is a computer algebra package written in REDUCE and it enables the obtaining of solutions of algebraic systems, ordinary, or partial differential equations with at most polynomial nonlinearity Homepage: http://lie.math.brocku.ca/Crack_demo.html Dependencies: REDUCE Keywords: integrable system; quadratic Hamiltonian; polynomial nonlinearity Related Software: REDUCE; LIEPDE; Maple; SYMMGRP; GeM; ConLaw; ApplySym; LIE; diffgrob2; SYMMGRP.MAX; SPDE; DIMSYM; BIGLIE; Mathematica; SADE; Janet; SINGULAR; PDEtools; DifferentialGeometry; CoCoA Cited in: 57 Documents Standard Articles 3 Publications describing the Software, including 3 Publications in zbMATH Year Applications of CRACK in the classification of integrable systems. Zbl 1073.37081Wolf, Thomas 2004 Size reduction and partial decoupling of systems of equations. Zbl 1049.68162Wolf, Thomas 2002 Examples of the investigation of differential equations with modularized programs. Zbl 0881.34001Wolf, T.; Brand, A. 1997 all top 5 Cited by 63 Authors 24 Wolf, Thomas Otto 6 Anco, Stephen C. 5 Bluman, George Wallace 3 Carminati, John 3 Cheviakov, Alexei F. 2 Ali, Sajid 2 Bokhari, Ashfaque H. 2 Brand, Andreas 2 Butcher, J. 2 Cheb-Terrab, Edgardo S. 2 Hereman, Willy A. 2 Hounkonnou, Mahouton Norbert 2 Huang, S.-L. Tracy 2 Kara, Abdul Hamid 2 Kiselev, Arthemy V. 2 Robertz, Daniel 1 Adams, Paul J. 1 Barco, M. A. 1 Broadbridge, Philip 1 Cimmelli, Vito Antonio 1 Clarkson, Peter A. 1 da Mota, Luis Antonio Campinho Pereira 1 Dkengne Sielenou, Pascal Alain 1 Doran-Wu, Patrick 1 Duarte, L. G. S. 1 Efimovskaya, O. V. 1 Eklund, Holly L. 1 Feng, Wei 1 Figueiredo, Annibal 1 Gatermann, Karin 1 Ghose Choudhury, Anindya 1 Guha, Partha 1 Herbst, Barend M. 1 Hickman, Mark S. 1 Jefferson, G. F. 1 Kashif, Abdul Rehman 1 Khanra, Barun 1 King, John Robert 1 Krasil’shchik, Joseph 1 Leach, Peter Gavin Lawrence 1 Lisle, Ian G. 1 Mohammadi, Zahra 1 Mohiuddin, Mohammad 1 Nakpim, Warisa 1 Nucci, Maria Clara 1 Oliveri, Francesco 1 Pace, Angelo Raffaele 1 Plesken, Wilhelm 1 Reid, Gregory John 1 Rocha Filho, Tarcísio M. 1 Roche, Austin D. 1 Rutz, Solange F. 1 Schrüfer, Eberhard 1 Sokolov, Vladimir Vyacheslavovich 1 Talati, Daryoush 1 Tsarev, Sergej Petrovich 1 Tsuchida, Takayuki 1 Turhan, Refik 1 Verbovetskiy, Alexander 1 Vitolo, Raffaele F. 1 Ward, Michael J. 1 Webster, Kenneth 1 Zaman, Fiazud Din all top 5 Cited in 23 Serials 8 Computer Physics Communications 4 Programming and Computer Software 3 General Relativity and Gravitation 3 Journal of Mathematical Analysis and Applications 3 Journal of Symbolic Computation 3 Mathematical and Computer Modelling 3 Mathematics in Computer Science 2 Journal of Engineering Mathematics 2 Journal of Mathematical Physics 2 Applied Mathematics and Computation 2 Acta Applicandae Mathematicae 2 Journal of Physics A: Mathematical and General 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Lecture Notes in Mathematics 1 Acta Mechanica 1 International Journal of Theoretical Physics 1 Letters in Mathematical Physics 1 Chaos, Solitons and Fractals 1 Mathematics and Computers in Simulation 1 Regular and Chaotic Dynamics 1 Applied Mathematical Sciences 1 Communications in Mathematical Analysis 1 Texts & Monographs in Symbolic Computation all top 5 Cited in 21 Fields 32 Partial differential equations (35-XX) 18 Computer science (68-XX) 17 Ordinary differential equations (34-XX) 17 Dynamical systems and ergodic theory (37-XX) 9 Numerical analysis (65-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Mechanics of particles and systems (70-XX) 5 Relativity and gravitational theory (83-XX) 4 Differential geometry (53-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Topological groups, Lie groups (22-XX) 3 Quantum theory (81-XX) 2 Special functions (33-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year