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

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  1. Mohammadi, Zahra; Reid, Gregory J.; Huang, S.-L. Tracy: Symmetry-based algorithms for invertible mappings of polynomially nonlinear PDE to linear PDE (2021)
  2. Krasil’shchik, Joseph; Verbovetskiy, Alexander; Vitolo, Raffaele: The symbolic computation of integrability structures for partial differential equations (2017)
  3. Cimmelli, Vito A.; Oliveri, F.; Pace, A. Raffaele: Phase-field evolution in Cahn-Hilliard-Korteweg fluids (2016)
  4. Nakpim, Warisa: Third-order ordinary differential equations equivalent to linear second-order ordinary differential equations via tangent transformations (2016)
  5. Talati, Daryoush; Turhan, Refik: Two-component integrable generalizations of Burgers equations with nondiagonal linearity (2016)
  6. Anco, Stephen C.; Feng, Wei; Wolf, Thomas: Exact solutions of semilinear radial Schrödinger equations by separation of group foliation variables (2015)
  7. Cheviakov, Alexei F.: Symbolic computation of nonlocal symmetries and nonlocal conservation laws of partial differential equations using the GeM package for Maple (2014)
  8. Robertz, Daniel: Formal algorithmic elimination for PDEs (2014)
  9. Anco, Stephen C.; Mohiuddin, Mohammad; Wolf, Thomas: Traveling waves and conservation laws for complex mKdV-type equations (2012)
  10. Vu, K. T.; Jefferson, G. F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
  11. Wolf, Thomas; Schrüfer, Eberhard; Webster, Kenneth: Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs (2012)
  12. Anco, Stephen C.; Ali, Sajid; Wolf, Thomas: Exact solutions of nonlinear partial differential equations by the method of group foliation reduction (2011)
  13. Anco, Stephen C.; Ali, S.; Wolf, Thomas: Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions (2011)
  14. Rocha Filho, Tarcísio M.; Figueiredo, Annibal: [SADE] a Maple package for the symmetry analysis of differential equations (2011)
  15. Wolf, T.: The parametric solution of underdetermined linear ODEs (2011)
  16. Bluman, G.; Broadbridge, P.; King, J. R.; Ward, M. J.: Similarity: Generalizations, applications and open problems (2010)
  17. Bluman, George W.; Cheviakov, Alexei; Anco, Stephen: Applications of symmetry methods to partial differential equations (2010)
  18. Cheviakov, Alexei F.: Symbolic computation of local symmetries of nonlinear and linear partial and ordinary differential equations (2010)
  19. Hounkonnou, Mahouton N.; Sielenou, Pascal D.: On time-space dependent conservation laws of nonlinear evolution differential equations (2010)
  20. Hounkonnou, M. N.; Sielenou, P. D.: Conservation laws for under determined systems of differential equations (2010)

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