TY - JOUR
T1 - Geometrical optics approximation for nonlinear equations
AU - Bass, F.
AU - Freilikher, V.
AU - Maradudin, A. A.
AU - Prosentsov, V.
PY - 2004/4
Y1 - 2004/4
N2 - A wide class of nonlinear equations is studied in the geometrical optics approximation. It is shown that a nonlinear equation with coefficients dependent on the amplitude of the function sought can be reduced to a system of quasi-linear equations of the gas-dynamics type. As an illustration, the Hamilton-Jacobi equation with a specific form of the nonlinear operator has been solved, and the propagation of monochromatic waves and of point source radiation in nonlinear media has been studied.
AB - A wide class of nonlinear equations is studied in the geometrical optics approximation. It is shown that a nonlinear equation with coefficients dependent on the amplitude of the function sought can be reduced to a system of quasi-linear equations of the gas-dynamics type. As an illustration, the Hamilton-Jacobi equation with a specific form of the nonlinear operator has been solved, and the propagation of monochromatic waves and of point source radiation in nonlinear media has been studied.
KW - Geometrical optics approximation
KW - Hamilton-Jacobi equation
KW - Nonlinear equations
KW - Quasi-linear equations
UR - http://www.scopus.com/inward/record.url?scp=4544364709&partnerID=8YFLogxK
U2 - 10.1137/s0036139903426617
DO - 10.1137/s0036139903426617
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AN - SCOPUS:4544364709
SN - 0036-1399
VL - 64
SP - 1125
EP - 1132
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 4
ER -