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Lie Symmetry Reductions and Exact Solutions to the Rosenau Equation
Advances in Mathematical Physics, 2014 The Lie symmetry analysis is performed on the Rosenau equation which arises in modeling many physical phenomena. The similarity reductions and exact solutions are presented. Then the exact analytic solutions are considered by the power series method.
Ben Gao, Hongxia Tian
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Symmetries of the Robinson-Trautman equation [PDF]
, 2006 We study point symmetries of the Robinson--Trautman equation. The cases of one- and two-dimensional algebras of infinitesimal symmetries are discussed in detail. The corresponding symmetry reductions of the equation are given.
Natorf, Wlodzimierz, Tafel, Jacek
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Adaptive Symmetry Reduction [PDF]
, 2007 Symmetry reduction is a technique to counter state explosion for systems of regular structure. It relies on idealistic assumptions about indistinguishable components, which in practice may only be similar. In this paper we present a generalized algebraic approach to symmetry reduction for exploring a structure without any prior knowledge about its ...
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AIMS MathematicsThis article represented the investigation of the modified mixed Korteweg-de Vries equation using different versatile approaches. First, the Lie point symmetry approach was used to determine all possible symmetry generators.
Nauman Raza +2 more
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Symmetry reduction for stochastic hybrid systems [PDF]
2008 47th IEEE Conference on Decision and Control, 2008 This paper is focused on adapting symmetry reduction, a technique that is highly successful in traditional model checking, to stochastic hybrid systems. To that end, we first show that performability analysis of stochastic hybrid systems can be reduced to a stochastic reachability analysis (SRA).
Bujorianu, L.M., Katoen, Joost P.
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Entropy, 2020 A conditional Lie-Bäcklund symmetry method and differential constraint method are developed to study the radially symmetric nonlinear convection-diffusion equations with source.
Lina Ji, Rui Wang
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The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies [PDF]
, 1996 The algebraic and Hamiltonian structures of the multicomponent dispersionless Benney and Toda hierarchies are studied. This is achieved by using a modified set of variables for which there is a symmetry between the basic fields.
Aoyama S +20 more
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Electronic Notes in Theoretical Computer Science, 2009 AbstractSymmetry reduction is an effective state-space reduction technique for model checking, and works by restricting search to equivalence class representatives with respect to a group of symmetries for a model. A major problem with symmetry reduction techniques is the time taken to compute the representative of a state, which can be prohibitive. In
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On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation [PDF]
, 2006 Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle $\theta$ are constructed and then reduced to the two-component Camassa--Holm model.
Aratyn, H. +2 more
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Point symmetries of generalized Toda field theories: II. Symmetry reduction [PDF]
Journal of Physics A: Mathematical and General, 2000 Summary: The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices, on one hand, and to periodic systems, on the other. Boundary conditions are introduced to reduce theories on an infinite lattice to those on semi-infinite or finite ones.
Martina, L. +2 more
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