Symmetry/Integrability Analysis and Computer Algebra for Nonlinear Differential Equations

Research - Groups

• Statistical Analysis and Computation Methods and Stochastic Models
• Symmetry/Integrability Analysis and Computer Algebra for Nonlinear Differential Equations
• Computational Methods for Variational Problems
• Analysis and Simulation of Discrete, Spatially-extended Dynamical Systems
• Computational Algebra and Number Theory
• Computer Algebra Algorithms and Parallel Computing
• Computational Topics in General Relativity, Gauge Theory, Classical Mechanics

Symmetry/Integrability Analysis and Computer Algebra for Nonlinear Differential Equations

S. Anco, T. Wolf and V. Sokolov have expertise as leaders in theory and symbolic computation for several modern aspects of differential equations: symmetries, integrability and solitons, conservation laws, classification of equations with formal geometric properties, applications to problems coming from applied mathematics, mathematical physics, as well as geometry.

Representative publications

1. G. Bluman and S.C. Anco, Symmetry and Integration Methods for Differential Equations, Springer-Verlag, Applied Mathematical Sciences series, volume 154, 2002.
2. S.C. Anco and S. Liu, “Exact solutions of semilinear radial wave equations in n dimensions”, J. Math. Analysis Appl. 297 (2004), 317-342.
3. S.C. Anco and G. Bluman, “Direct construction method for conservation laws of partial differential equations I: Examples of conservation law classifications. and II: General treatment”, Euro. Jour. Applied Math. 13 (2002), 545-566 and 567-585.
4. S.C. Anco, “Conservation laws of scaling-invariant field equations”, J. Phys. A: Math. and Gen. 36 (2003), 8623-8638.
5. T. Wolf, “A comparison of four approaches to the calculation of conservation laws”, Euro. Jour. Applied Math. 13 part 2 (2002), 129-152.
6. T. Wolf and O.V. Efimovskaya, “Classification of integrable quadratic Hamiltonians on e(3)”, Regular and Chaotic Dynamics, 8, no 2 (2003), 155-162.
7. V.V. Sokolov and T. Wolf, “Classification of integrable polynomial vector evolution equations”, J. Phys. A: Math. Gen. 34 (2001), 11139-11148.
8. S.C. Anco and T. Wolf, "Some symmetry classifications of hyperbolic vector evolution equations", J. Nonlinear Math. Phys. 12, Supplement 1 (2005), 13-31; erratum, J. Nonlinear Math. Phys. 12 (2005), 607-608.