CRACK
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
Keywords for this software
References in zbMATH (referenced in 56 articles , 3 standard articles )
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Sorted by year (- Krasil’shchik, Joseph; Verbovetskiy, Alexander; Vitolo, Raffaele: The symbolic computation of integrability structures for partial differential equations (2017)
- Cimmelli, Vito A.; Oliveri, F.; Pace, A. Raffaele: Phase-field evolution in Cahn-Hilliard-Korteweg fluids (2016)
- Nakpim, Warisa: Third-order ordinary differential equations equivalent to linear second-order ordinary differential equations via tangent transformations (2016)
- Talati, Daryoush; Turhan, Refik: Two-component integrable generalizations of Burgers equations with nondiagonal linearity (2016)
- Anco, Stephen C.; Feng, Wei; Wolf, Thomas: Exact solutions of semilinear radial Schrödinger equations by separation of group foliation variables (2015)
- Cheviakov, Alexei F.: Symbolic computation of nonlocal symmetries and nonlocal conservation laws of partial differential equations using the GeM package for Maple (2014)
- Robertz, Daniel: Formal algorithmic elimination for PDEs (2014)
- Anco, Stephen C.; Mohiuddin, Mohammad; Wolf, Thomas: Traveling waves and conservation laws for complex mKdV-type equations (2012)
- Vu, K. T.; Jefferson, G. F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
- Wolf, Thomas; Schrüfer, Eberhard; Webster, Kenneth: Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs (2012)
- Anco, Stephen C.; Ali, Sajid; Wolf, Thomas: Exact solutions of nonlinear partial differential equations by the method of group foliation reduction (2011)
- Anco, Stephen C.; Ali, S.; Wolf, Thomas: Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions (2011)
- Rocha Filho, Tarcísio M.; Figueiredo, Annibal: [SADE] a Maple package for the symmetry analysis of differential equations (2011)
- Wolf, T.: The parametric solution of underdetermined linear ODEs (2011)
- Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.: Similarity: Generalizations, applications and open problems (2010)
- Bluman, George W.; Cheviakov, Alexei; Anco, Stephen: Applications of symmetry methods to partial differential equations (2010)
- Cheviakov, Alexei F.: Symbolic computation of local symmetries of nonlinear and linear partial and ordinary differential equations (2010)
- Hounkonnou, Mahouton N.; Sielenou, Pascal D.: On time-space dependent conservation laws of nonlinear evolution differential equations (2010)
- Hounkonnou, M. N.; Sielenou, P. D.: Conservation laws for under determined systems of differential equations (2010)
- Lisle, Ian; Huang, S.-L. Tracy: Algorithmic symmetry classification with invariance (2010)