CONSLAW swMATH ID: 155 Software Authors: Yao, Ruo-Xia; Li, Zhi-Bin Description: An improved algorithm to explicitly compute the polynomial-type conservation laws for nonlinear evolution equations (either uniform in rank or not) is introduced and a software package CONSLAW written in Maple to automate the computation is developed. CONSLAW can construct the polynomial-type conservation laws for polynomial partial differential equations automatically. Furthermore, some new integrable systems can be filtered out by analyzing the compatibility conditions, which guarantee the existence of the conservation laws for a given parameterized nonlinear evolution equations. The explicit forms of the conserved densities play an important role in studying the integrability, such as explicit analytical solutions, bi-Hamiltonian form, one-parameter family of B\"acklund transformations, Lax pairs, and the checking of the accuracy of numerical integration algorithm. The effectiveness of CONSLAW is illustrated by applying it to a variety of equations. Homepage: http://www.springerlink.com/content/h203541633406r87/fulltext.pdf Dependencies: Maple Keywords: nonlinear evolution equation; scaling symmetry; conservation laws; symbolic computation; Korteweg-de Vries equation; numerical examples; Boussinesq equation; algorithm; software package CONSLAW; integrable systems; B\"acklund transformations; Lax pairs Related Software: Maple; CONDENS; GeM; WKPtest; PSEUDO; JACOBI; DDESpecialSolutions; CLawDDEs; DifferentialGeometry; DDEDensityFlux; FDCD; Vessiot; ConLaw; Rif; InvariantsSymmetries; TransPDEDensityFlux; CRACK; REDUCE; Mathematica; ATFM Cited in: 7 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year CONSLAW: A Maple package to construct the conservation laws for nonlinear evolution equations. Zbl 1090.65124Yao, Ruo-Xia; Li, Zhi-Bin 2006 all top 5 Cited by 12 Authors 4 Li, Zhibin 3 Yao, Ruoxia 1 Adams, Paul J. 1 Eklund, Holly L. 1 Fu, Jingzhi 1 Herbst, Barend M. 1 Hereman, Willy A. 1 Hickman, Mark S. 1 Liu, Yinping 1 Tu, Guizhang 1 Zhou, Zhenjiang 1 Zhu, Jiaofeng Cited in 4 Serials 2 Applied Mathematics and Computation 1 International Journal of Modern Physics B 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Systems Science and Complexity all top 5 Cited in 6 Fields 6 Partial differential equations (35-XX) 6 Computer science (68-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Ordinary differential equations (34-XX) 2 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year