Direct approach to the periodic solutions of the multidimensional sine–Gordon equation
- 1 January 1983
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 24 (1) , 46-52
- https://doi.org/10.1063/1.525601
Abstract
A number of identities for multidimensional theta functions and their derivatives are derived. Application to the nonlinear partial differential equations is exemplified for the sine–Gordon equation. In consequence, the multidimensional sine–Gordon equation can be reduced to a functional equation, and then to a set of algebraic equations. Several particular cases are also discussed.Keywords
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