Analytical Solution of the Boundary-Value Problem for the Nonlinear Helmholtz Equation
- 1 March 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (3) , 824-826
- https://doi.org/10.1063/1.1665218
Abstract
A rigorous analytical solution in terms of the elliptic integral function of the first kind is derived for the nonlinear inhomogeneous boundary‐value problem δ(d2f/dx2) = αf2 − εf − σ, f(s) = f̃.Keywords
This publication has 3 references indexed in Scilit:
- Expansion Method for Nonlinear Boundary-Value ProblemsJournal of Mathematical Physics, 1967
- On the theory of non-linear differential Equations of Parabolic type. IIMathematische Zeitschrift, 1936
- Zur Theorie der nichtlinearen partiellen Differentialgleichungen vom parabolischen TypusMathematische Zeitschrift, 1932