Bäcklund generated solutions of Liouville’s equation and their graphical representations in three spatial dimensions

DOI10.1063/1.525565zbMath0493.35073OpenAlexW2076827055MaRDI QIDQ3955784

Shein-Shion Wang, George Leibbrandt, Nader G. Zamani

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1063/1.525565

zbMATH Keywords

multiple solutionshigher dimensionsBäcklund transformationLiouville equationnonlinear superpositionring singularity

Mathematics Subject Classification ID

Nonlinear higher-order PDEs (35G20) Partial differential equations of mathematical physics and other areas of application (35Q99) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (5)

Linearization of nonlinear differential equations by means of Cauchy’s integral ⋮ Exact solutions for the nonlinear Klein–Gordon and Liouville equations in four-dimensional Euclidean space ⋮ Wronskians, geometry, and some general solutions to the nonlinear Liouville-like PDE’s ⋮ Nonlinear electrostatics: the Poisson–Boltzmann equation ⋮ The Bäcklund transformation and nonlinear superposition formula of solutions for the Liouville's equation in higher dimensions

Cites Work

• Nonlinear superposition for Liouville's equation in three spatial dimensions
• Singular solutions of the equation (d'Alembert operator) \(\phi+(m^ 2/2)\exp \phi=0\) and dynamics of singularities
• Vortices, Liouville's equation and the Bergman kernel function
• Solutions of the sine-Gordon equation in higher dimensions

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