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Mathematics, 2020 In this work, we investigate a (3+1)-dimensional generalised Kadomtsev–Petviashvili equation, recently introduced in the literature. We determine its group invariant solutions by employing Lie symmetry methods and obtain elliptic, rational and ...
Innocent Simbanefayi +1 more
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Advances in Nonlinear Analysis, 2023 In the present work, we find the Lie point symmetries of the Ricci flow on an n-dimensional manifold, and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics.
López Enrique +2 more
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Weak transversality and partially invariant solutions [PDF]
Journal of Mathematical Physics, 2003 New exact solutions are obtained for several nonlinear physical equations, namely the Navier–Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schrödinger equation. The solution method makes use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.
Grundland, A. M. +2 more
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DUALITY INVARIANCE OF COSMOLOGICAL SOLUTIONS WITH TORSION [PDF]
International Journal of Modern Physics A, 1999 We show that for a string moving in a background consisting of maximally symmetric gravity, dilaton field and second rank antisymmetric tensor field, the O(d) ⊗ O(d) transformation on the vacuum solutions gives inequivalent solutions that are not maximally symmetric.
Gangopadhyay, Debashis +1 more
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Frontiers in Physics, 2020 The variable-coefficient Heisenberg ferromagnetic spin chain (vcHFSC) equation is investigated using the Lie group method. The infinitesimal generators and Lie point symmetries are reported.
Na Liu, Na Liu
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The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic [PDF]
, 2016 Let G be a Sylow p -subgroup of the unitary groups GU(3,q2)GU(3,q2), GU(4,q2)GU(4,q2), the symplectic group Sp(4,q)Sp(4,q) and, for q odd, the orthogonal group O+(4,q)O+(4,q).
Fleischmann, Peter +2 more
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Riemann Invariants and Rank-k Solutions of Hyperbolic Systems [PDF]
, 2006 In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions.
Huard, Benoit, Grundland, A. Michel
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Mathematical and Computational Applications, 2023 We used the classical Lie symmetry method to study the damped Klein–Gordon equation (Kge) with power law non-linearity utt+α(u)ut=(uβux)x+f(u). We carried out a complete Lie symmetry classification by finding forms for α(u) and f(u).
Fiazuddin D. Zaman +2 more
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Invariance of Solutions to Invariant Nonparametric Variational Problems [PDF]
Transactions of the American Mathematical Society, 1980 Let G be a compact Lie group of diffeomorphisms of a connected orientable manifold M of dimension n +
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Square-integrability of solutions of the Yamabe equation [PDF]
, 2011 We show that solutions of the Yamabe equation on certain n- dimensional non-compact Riemannian manifolds which are bounded and Lp for p = 2n=(n-2) are also L2. This Lp-L2-implication provides explicit constants in the surgery-monotonicity formula for the
Humbert, Emmanuel +3 more
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