Exact solutions for the nonlinear Klein–Gordon and Liouville equations in four-dimensional Euclidean space

DOI10.1063/1.527764zbMath0663.35077OpenAlexW2057953211MaRDI QIDQ3812669

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Publication date: 1987

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527764

zbMATH Keywords

exact solutionsLiouville equationsnonlinear Klein-Gordon equationsymmetry variables

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Partial differential equations of mathematical physics and other areas of application (35Q99) Solutions to PDEs in closed form (35C05)

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Solving multi-linear systems with \(\mathcal {M}\)-tensors ⋮ Conjugate gradient-like methods for solving general tensor equation with Einstein product ⋮ The accelerated overrelaxation splitting method for solving symmetric tensor equations ⋮ Compactification of two dimensions in general relativity ⋮ A two-step accelerated Levenberg-Marquardt method for solving multilinear systems in tensor-train format ⋮ Conformally flat spacetimes and Weyl frames ⋮ Isogroups and exact solutions for some Klein–Gordon and Liouville-type equations in n-dimensional Euclidean space ⋮ Alternating iterative methods for solving tensor equations with applications ⋮ Wronskians, geometry, and some general solutions to the nonlinear Liouville-like PDE’s ⋮ Nonlinear electrostatics: the Poisson–Boltzmann equation ⋮ A globally and quadratically convergent algorithm for solving multilinear systems with \(\mathcal {M}\)-tensors ⋮ A proximal point like method for solving tensor least-squares problems ⋮ Tensor Bi-CR Methods for Solutions of High Order Tensor Equation Accompanied by Einstein Product

Cites Work

• On the classical solutions of the Liouville equation in a four- dimensional Euclidean space
• Classical solutions and the energy-momentum tensor
• Symmetry reduction for nonlinear relativistically invariant equations
• Bäcklund generated solutions of Liouville’s equation and their graphical representations in three spatial dimensions

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