Exact solution to a nonlinear Klein--Gordon equation

Journal Article · Tue Jul 01 04:00:00 EDT 1975 · J. Math. Anal. Appl.; (United States)

OSTI ID:7352591

Burt, P B; Reid, J L

The nonlinear Klein-Gordon equation delta ..mu.. delta/sub ..mu../PHI + M/sup 2/PHI + lambda/sub 1/ PHI/sup 1-m/ + lambda/sub 2/ PHI/sup 1-2m/ = 0 has the exact formal solution PHI = (u/sup 2m/ - lamdba/sub 1/ u/sup m//(m - 2)M/sup 2/ + lambda/sub 1//sup 2//(m - 2)/sup 2/M/sup 4/ - lambda/sub 2//4(m - 1)M/sup 2/)/sup 1/m/u/sup -1/, m is not equal to 0,1,2, where u and u/sup -1/ are solutions of the linear Klein-Gordon equation. This equation is a simple generalization of the ordinary second order differential equation satisfied by the homogeneous function y = (au/sup m/ + b(uv)/sup m/2/ + cv/sup m/)/sup k/m/, where u and v are linearly independent solutions of y'' + r(x)y' + q(x)y = 0.

• Research Organization: Clemson Univ., SC
• OSTI ID: 7352591
• Journal Information: J. Math. Anal. Appl.; (United States), Journal Name: J. Math. Anal. Appl.; (United States) Vol. 55:1; ISSN JMANA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
KLEIN-GORDON EQUATION
NONLINEAR PROBLEMS
QUANTUM FIELD THEORY
WAVE EQUATIONS