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Separability and Lax pairs for Hénon–Heiles system
Journal of Mathematical Physics, 1993The Hamiltonian system corresponding to the (generalized) Hénon–Heiles Hamiltonian H= 1/2(px2+py2)+1/2Ax2+1/2By2+x2y+εy3 is known to be integrable in the following three cases: (A=B, ε=1/3); (ε=2); (B=16A, ε=16/3). In the first two the system has been integrated by making use of genus one and genus two theta functions.
Ravoson, V., Gavrilov, L., Caboz, R.
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An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems
Physics Letters A, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ma, Wenxiu, Strampp, Walter
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A note on the Lax pairs for Painlevéequations
Journal of Physics A: Mathematical and General, 1999The Painlevé equations PI-PVI are six genuine nonlinear second-order differential equations such that the only movable singularities of their solutions are poles. By definition, movable singular are points which change when the initial conditions are changed.
Kapaev, A. A., Hubert, E.
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Constraint of discrete Lax equations with some special types of Lax pairs
2011 International Conference on Multimedia Technology, 2011In this paper, firstly we deduce the constraint of discrete Lax equations with some special forms of Lax pairs. Then to illustrate the validity of the method, we construct two discrete Lax equations and successfully obtain their constraints by the method.
null Nianhua Li +3 more
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A Lax pair of the discrete Euler top
, 2016We proposed the discrete Euler top in 2000. In that paper, exact solutions and conserved quantities are described. However, a Lax pair of our proposed discrete Euler top is not contained. Moreover, the Lax pair is still unknown.
Kinji Kimura
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