Nonlinear eigenvalue problems for Maxwells equations.
Main publications:
Valovik D.V., “On the problem of nonlinear coupled electromagnetic transverse-
electric.transverse-magnetic wave propagation”, Journal of Mathematical Physics, 54:4 (2013), 042902 (14 pages)
Valovik D.V., “Integral dispersion equation method to solve a nonlinear boundary eigenvalue problem”, Nonlinear Analysis: Real World Applications, 20 (2014), 52–58
Smirnov Yu.G., Valovik D.V., “Guided electromagnetic waves propagating in a plane dielectric waveguide with nonlinear permittivity”, Physical Review A, 92:1 (2015), 013840 (6 pages)
Smirnov Yu.G., Valovik D.V., “On the infinitely many nonperturbative solutions in a
transmission eigenvalue problem for Maxwell.s equations with cubic nonlinearity”, Journal of Mathematical Physics, 57:10 (2016), 103504 (15 pages)
Valovik D.V., “Novel propagation regimes for TE waves guided by a waveguide filled with
Kerr medium”, Journal of Nonlinear Optical Physics & Materials, 25:4 (2016), 1650051 (17 pages)
ISTINA
