Journal of Nonlinear Mathematical Physics · 1999 · 64 citations · 15 references
Natural SciencesMathematicsPhysicsDifferential EquationsIntegrable SystemsPartial Differential EquationsSystems Of Differential EquationsCompletely Integrable SystemsIntegrable Partial Differential EquationsKdv EquationKorteweg - De Vries EquationLax PairsPainlevé Equations
It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlevé test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax pairs, whereas for one case it remains unknown.
15
Applications of lie groups to differential equations
Acta Applicandae Mathematicae · 1990 · 6.1K citations
The Painlevé property for partial differential equations
John Weiss, M. Tabor, G. F. Carnevale · Journal of Mathematical Physics · 1983 · 2.1K citations
Soliton solutions of a coupled Korteweg-de Vries equation
Ryogo Hirota, Junkichi Satsuma · Physics Letters A · 1981 · 823 citations