Higher conditional symmetry and reduction of initial value problems

Nonlinear Dynamics

Volumn 28, Issue 1, 2002, Pages 17-27

  Zhdanov, R Z ^a  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

Author keywords

Cauchy problem; Conditional symmetry; Nonlinear evolution equation; Reduction

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; VECTORS;

CAUCHY PROBLEM; CONDITIONAL SYMMETRY; EQUATION REDUCTION; NONLINEAR EVOLUTION EQUATION;

INITIAL VALUE PROBLEMS;

EID: 0036537869     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014962601569     Document Type: Article

References (27)

1. The general similarity solution of the heat equation
2. On a reduction and solutions of nonlinear wave equations with broken symmetry
3. Reduction of differential equations and conditional symmetry
4. Precise definition of reduction of partial differential equations
5. On new exact blow-up solutions for nonlinear heat conduction equations with source and applications
6. Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities
7. Anti-reduction of the nonlinear wave equation
8. Conditional symmetry and anti-reduction of nonlinear heat equation
9. Conditional Lie-Bäcklund symmetry and reduction of evolution equations
10. Generalized conditional symmetries and exact solutions of non-integrable equations
11. Direct reduction and differential constraints
12. Lie-Backlund symmtries of linear ODEs and generalized separation of variables in nonlinear equations
13. Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems
14. Group classification and generalized conditional symmetry reduction of the nonlinear diffusion-convection equation with a nonlinear source
15. Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries
16. Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
17. Higher conditional symmetries and reduction of initial value problems
18. Non-classical reductions of initial-value problems for a class of nonlinear evolution equations
19. Initial-value problems for evolution partial differential equations and higher-order conditional symmetries