Accession Number : ADA193475

Title :   The Construction of Implicit and Explicit Solitary Wave Solutions of Nonlinear Partial Differential Equations.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES

Personal Author(s) : Hereman, Willy

PDF Url : ADA193475

Report Date : Aug 1987

Pagination or Media Count : 23

Abstract : By means of easy examples, such as the Korteweg-de Vries, the Harry Dym, the sine-Gordon equations, and the Hirota coupled system, it is shown how nonlinear partial differential equations can be exactly solved by a direct algebraic method. The physical concept, on which the method relies, is one of generation and mixing of the real exponential solutions of the underlying linear equations. This approach leads in a straightforward way to single solitary waves of pulse, kink and cusp shape. The extension of the method towards the construction of multi-soliton solutions and the connections with other direct methods are outlined.

Descriptors :   *NONLINEAR DIFFERENTIAL EQUATIONS, *PARTIAL DIFFERENTIAL EQUATIONS, ALGEBRA, COUPLING(INTERACTION), LINEAR ALGEBRAIC EQUATIONS, PHYSICAL PROPERTIES, PULSES, SHAPE, SOLUTIONS(GENERAL), WAVES

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE