Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs. This paper discusses the algorithms and implementations of three MATHEMATICA packages for the study of integrability and the computation of closed-form solutions of nonlinear polynomial partial differential equations (PDEs). The first package, PainleveTest.m, symbolically performs the Painlevé integrability test. The second package, PDESpecialSolutions.m, computes exact solutions expressible in hyperbolic or elliptic functions. The third package, PDERecursionOperator.m, generates and tests recursion operators.

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  1. Jiang, Liya; Jin, Yongyang; Ma, Wen-Xiu; Shen, Shoufeng; Zhu, Haiyan: Novel soliton hierarchies of Levi type and their bi-Hamiltonian structures (2015)
  2. Shen, Shoufeng; Jiang, Liya; Jin, Yongyang; Ma, Wen-Xiu: New soliton hierarchies associated with the Lie algebra so(3,$\BbbR$) and their Bi-Hamiltonian structures (2015)
  3. Wang, Yun-Po; Tian, Bo; Wang, Ming; Wang, Yu-Feng; Sun, Ya; Xie, Xi-Yang: Bäcklund transformations and soliton solutions for a $(2+1)$-dimensional Korteweg-de Vries-type equation in water waves (2015)
  4. Zhu, Haiyan; Yu, Shuimeng; Shen, Shoufeng; Ma, Wen-Xiu: New integrable $\mathrmsl(2,\mathbbR)$-generalization of the classical Wadati-Konno-Ichikawa hierarchy (2015)
  5. Ma, Wen-Xiu: A soliton hierarchy associated with $\mathrmso(3,\mathbb R)$ (2013)
  6. Naz, Rehana; Naeem, Imran; Khan, M.Danish: Conservation laws of some physical models via symbolic package GeM (2013)
  7. Wazwaz, Abdul-Majid: $(2+1)$-dimensional mKdV (N) equations by the mKdV recursion operator: multiple soliton and multiple singular soliton solutions (2012)
  8. Poole, Douglas; Hereman, Willy: Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions (2011)
  9. Bagchi, Bijan; Das, Supratim; Ganguly, Asish: New exact solutions of a generalized shallow water wave equation (2010)
  10. Baldwin, D.E.; Hereman, W.: A symbolic algorithm for computing recursion operators of nonlinear partial differential equations (2010)
  11. Picard, P.Y.: Some exact solutions of the ideal MHD equations through symmetry reduction method (2008)
  12. Baldwin, D.; Hereman, W.; Sayers, J.: Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs (2005)