TY - JOUR
T1 - Propagators for non-linear systems
AU - Cacuci, D. G.
AU - Protopopescu, V.
PY - 1989
Y1 - 1989
N2 - A canonical formalism based on forward and backward propagators is developed for problems described by systems of general non-linear equations. These propagators are shown to yield the problem's solution by propagating exactly the bulk/surface/initial sources. They naturally generalise to non-linear problems the Green functions of linear theory. Unlike the customary Green functions, though, the forward and backward propagators depend parametrically and non-linearly on the problem's solution; however, the propagators themselves satisfy linear equations that can, in principle, be solved by methods of linear theory. Three examples, comprising both scalar and vector problems, are presented to highlight the main points underlying the application of this formalism.
AB - A canonical formalism based on forward and backward propagators is developed for problems described by systems of general non-linear equations. These propagators are shown to yield the problem's solution by propagating exactly the bulk/surface/initial sources. They naturally generalise to non-linear problems the Green functions of linear theory. Unlike the customary Green functions, though, the forward and backward propagators depend parametrically and non-linearly on the problem's solution; however, the propagators themselves satisfy linear equations that can, in principle, be solved by methods of linear theory. Three examples, comprising both scalar and vector problems, are presented to highlight the main points underlying the application of this formalism.
UR - http://www.scopus.com/inward/record.url?scp=42549173610&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/22/13/033
DO - 10.1088/0305-4470/22/13/033
M3 - Article
AN - SCOPUS:42549173610
SN - 0305-4470
VL - 22
SP - 2399
EP - 2414
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 13
M1 - 033
ER -