Computer Algebra Application for Classification of Integrable Non-Linear Evolution Equations

@article{Gerdt1985ComputerAA,
  title={Computer Algebra Application for Classification of Integrable Non-Linear Evolution Equations},
  author={Vladimir P. Gerdt and A. B. Shvachka and A. Yu. Zharkov},
  journal={J. Symb. Comput.},
  year={1985},
  volume={1},
  pages={101-107}
}
Different criteria of integrability are used for the classification of equations (1): the existence of non-trivial symmetries (Fokas, 1980; Fujimoto & Watanabe, 1983), conservation laws (Abellanas & Galindo, 1983), prolongation structures (Leo et al., 1983). In this paper we shall describe a classification method based on the concept of formal integrability (Ibragimov & Shabat, 1980b). The latter is one of the strict formulations of the concept of L A pair (Lax, 1968). Formal integrability puts… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 19 references

On the B[icklund transformations for integrable evolution equations

S. I. Svinolupov, V. V. Sokolov, R. I. Yamilov
DAN SSSR, • 1983
View 4 Excerpts
Highly Influenced

On the B~tcklund

N. H. Ibragimov, A. B. Shabat
1980
View 5 Excerpts
Highly Influenced

On the infinite Lie-B/icklund algebras

N. H. Ibragimov, A. B. Shabat
Funct. Anal 14, • 1980
View 5 Excerpts
Highly Influenced

A symmetry approach to exactly solvable evolution equations

A. S. Fokas
J. Math. Phys • 1980
View 4 Excerpts
Highly Influenced

Gr 6 bner bases : an algorithmic method in polynomial ideal theory

B. Buchberger
Recent Trends in Multidimensional Systems Theory • 1985
View 1 Excerpt

Gr6bner bases: an algorithmic method in polynomial ideal theory. In: Recent Trends

B. Buchberger
1985
View 2 Excerpts

Classification of fifth-order evolution equations with nontrivial symmetries

A. Fujimoto, Y. Watanabe
Math . Jap • 1983
View 1 Excerpt

Evolution equations with high-order conservation laws

L. A. Abellanas, A. Galindo
J. Math. Phys • 1983
View 2 Excerpts

Nonlinear evolution equations and nonabelian prolongations

M. Leo, R. A. Leo, G. Soliani, L. Solombrino, L. Martina
J: Math. Phys • 1983
View 1 Excerpt

REDUCE - 2 program for investigating integrability of nonlinear evolution equations

A. Yu. Zharkov, A. B. Shvaehka
1983

Similar Papers

Loading similar papers…