Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 713-724
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An iterative method is proposed to determine the eigenfunctions of a system of two nonlinear Schrödinger equations governing the interaction of two femtosecond pulses in a medium with quadratic and cubic nonlinearity. The method produces soliton solutions of a new form for a wide range of nonlinearity coefficients corresponding to the first and second eigenvalues. A specially chosen initial approximation is required to determine the third and higher eigenfunctions.
@article{ZVMMF_2008_48_4_a13,
author = {O. V. Matusevich and V. A. Trofimov},
title = {Iterative method for finding the eigenfunctions of a~system of two {Schr\"odinger} equations with combined nonlinearity},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {713--724},
publisher = {mathdoc},
volume = {48},
number = {4},
year = {2008},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a13/}
}
TY - JOUR AU - O. V. Matusevich AU - V. A. Trofimov TI - Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2008 SP - 713 EP - 724 VL - 48 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a13/ LA - ru ID - ZVMMF_2008_48_4_a13 ER -
%0 Journal Article %A O. V. Matusevich %A V. A. Trofimov %T Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2008 %P 713-724 %V 48 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a13/ %G ru %F ZVMMF_2008_48_4_a13
O. V. Matusevich; V. A. Trofimov. Iterative method for finding the eigenfunctions of a system of two Schrödinger equations with combined nonlinearity. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 4, pp. 713-724. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_4_a13/