
Accession Number : AD0707798
Title : EXTREMUM PRINCIPLES FOR THE EQUATION DEL SQUARED PHI = PHI  (PHI CUBED).
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Robinson,Peter D.
Report Date : DEC 1969
Pagination or Media Count : 21
Abstract : The Lagrangian functional G(phi) = the integral of ((1/2)phi((del squared)+1)phi (1/4)(phi to the 4th power))dr is shown to be an upper bound for G(phi sub 0), where phi sub 0 is the groundstate eigenfunction of (del squared)phi + phi  (phi cubed) = 0, provided that G(phi) is stationary with respect to amplitude or scale variations in phi. Complementary functionals are also shown to provide upper bounds. (Author)
Descriptors : (*CALCULUS OF VARIATIONS, FIELD THEORY), WAVE FUNCTIONS, PARTIAL DIFFERENTIAL EQUATIONS, ELEMENTARY PARTICLES, ELECTROMAGNETIC FIELDS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE