Accession Number : AD0837031

Title :   ON THE STABILITY OF SOLUTIONS OF A NONLINEAR FIELD EQUATION.

Descriptive Note : Master's thesis,

Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA

Personal Author(s) : Davis, William Joseph

Report Date : JUN 1968

Pagination or Media Count : 65

Abstract : Solutions to a nonlinear wave equation were analyzed for their stability. The wave equation is a Klein-Gordon equation with the mass replaced by the square of the wave function. This wave equation has propagating solutions which are unbounded or periodic, depending on the sign of the nonlinear term and the propagation speed which can be sub- or super-light velocity. The stability of the periodic sub-light velocity solution was investigated by the method of characteristic exponents and was found to be indifferent. Liapounoff's direct method and Sturrock's analysis of the dispersion relation combined with a WKB technique were applied to a linearized perturbation on a static solution of the field equation. The periodic solution with beta squared < 1 is stable, while the method of characteristic exponents gives indifference. The super-light velocity solutions are unstable. Due to the limitations of the approximations, it could not be determined whether the instability is absolute or convective. (Author)

Descriptors :   *NONLINEAR DIFFERENTIAL EQUATIONS), (*ELEMENTARY PARTICLES, WAVE FUNCTIONS, PARTIAL DIFFERENTIAL EQUATIONS, APPROXIMATION(MATHEMATICS), PERTURBATION THEORY, PERIODIC VARIATIONS, POTENTIAL THEORY, FIELD THEORY, STABILITY, THESES.

Subject Categories : Theoretical Mathematics
      Nuclear Physics & Elementary Particle Physics

Distribution Statement : APPROVED FOR PUBLIC RELEASE