The ladder problem: Painlevé integrability and explicit solution

“…The constraints of the latter so that it is integrable in terms of analytic functions are determined by the imposition of a like Abelian algebra. The integrability of the ladder system in terms of the Painlevé analysis, explicit reduction and generation of solutions was given recently [3].…”

Section: Ladder Systemsmentioning

confidence: 99%

“…The ladder system has certain general properties [3,5,6]. According to [3] the rank of the matrix A is two for n > 2 and the n-dimensional ladder system can be considered as the simplest Riccati equation for n i=1 x i and as such is an example of a decomposed system [4].…”

Section: Ladder Systemsmentioning

confidence: 99%

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The complete symmetry group of the generalised hyperladder problem

Andriopoulos¹

2004

Journal of Mathematical Analysis and Applications

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We further consider the n-dimensional ladder system, that is the homogeneous quadratic system of first-order differential equations of the formẋ i = x i n j =1 a ij x j , i = 1, n, where (a ij ) = (i + 1 − j), i, j = 1, n introduced by Imai and Hirata (nlin.SI/0212007). We establish the most general system of first-order ordinary differential equations invariant under the algebra which characterises the ladder system of Imai and Hirata and the algebra of minimal dimension required to specify completely this most general system. We provide the complete symmetry group of the generalised hyperladder system and discuss its integrability.  2004 Elsevier Inc. All rights reserved. Ladder systemsIn two recent papers Imai and Hirata developed a necessary condition for the existence of Lie point symmetries in n-dimensional systems of first-order ordinary differential equations [5] and applied the ideas developed there to establish a new integrable family in the class of Lotka-Volterra systems [6]. Of the infinite number of Lie symmetries that such a

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“…In the case of systems of linear first-order ordinary differential equations a generalised self-similar symmetry is an obvious symmetry to be considered since there is by definition similarity in the dependent variables and so one has only to determine how the independent variable comes into the symmetry. For examples of a different type of constraint see [1,9,10].…”

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confidence: 99%

Generalised Symmetries and the Ermakov-Lewis Invariant

Goodall

2005

JNMP

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Generalised symmetries and point symmetries coincide for systems of first-order ordinary differential equations and are infinite in number. Systems of linear first-order ordinary differential equations possess a generalised rescaling symmetry. For the system of first-order ordinary differential equations corresponding to the time-dependent linear oscillator the invariant of this symmetry has the form of the famous ErmakovLewis invariant, but in fact reveals a richer structure.

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The ladder problem: Painlevé integrability and explicit solution

Cited by 15 publications

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Singularity Analysis and Integrability of a Simplified Multistrain Model for the Transmission of Tuberculosis and Dengue Fever

Singularity Analysis and Integrability of a Simplified Multistrain Model for the Transmission of Tuberculosis and Dengue Fever

The complete symmetry group of the generalised hyperladder problem

Generalised Symmetries and the Ermakov-Lewis Invariant

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