Exact solutions of the \(m\)-dimensional wave equation from paraxial ones. Further generalizations of the Bateman solution
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Publication:1930254
DOI10.1007/S10958-012-0944-7zbMath1256.35151OpenAlexW2091722768MaRDI QIDQ1930254
Publication date: 10 January 2013
Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10958-012-0944-7
PDEs in connection with optics and electromagnetic theory (35Q60) Wave equation (35L05) Lasers, masers, optical bistability, nonlinear optics (78A60) Second-order hyperbolic equations (35L10) Solutions to PDEs in closed form (35C05)
Related Items (7)
On astigmatic exponentially localized solutions for the wave and the Klein–Gordon–Fock equations ⋮ Tilted nonparaxail beams and packets for the wave equation with two spatial variables ⋮ Simple solutions of the wave equation with a singularity at a running point, based on the complexified Bateman solution ⋮ Two-dimensional singular splash pulses ⋮ Spherical Generalized Functional-Invariant Solutions to the Wave Equation ⋮ Bateman-Hörmander two-dimensional waves with a singularity at a running point ⋮ On the Bateman-Hörmander solution of the wave equation having a singularity at a running point
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- A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation
- The connection between the solutions of the Helmholtz equation and those of Schrödinger type equations
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