Effective Numerical Methods for Simulating (2+1)D Three Wave Mixing

Article type: Research Article

Authors: Chuprakov, D.A.^a | Kalinovich, A.A.^{a; 1} | Sukhorukov, A.P.^a | Zakharova, I.G.^b

Affiliations: [a] Physics Faculty, Lomonosov Moscow State University, Vorobiovy gory, 119899 Moscow, Russia. E-mail: [email protected], [email protected], [email protected] | [b] Institute for Mathematical Modeling RAS, Miusskaya sq.4-A, 125047 Moscow, Russia. E-mail: [email protected]

Correspondence: [1] The address for manuscript correspondence: A. A. Kalinovich, Physics Faculty, Lomonosov Moscow State University, Vorobiovy gory, 119899, Moscow, Russia. E-mail: [email protected]. Tel.: (7-095) 939-3317.

Abstract: The transparent boundary condition method (TBCM) is applied to solving the problem of three-wave mixing. The difference analogs of invariants (DAI) are shown to be conserved with optimal decrease of the transverse mesh step rather than the longitudinal one. The implemented numerical simulation demonstrated the efficiency of the considered approaches.

Keywords: Wave mixing, boundary condition, vortex, soliton, trapping, invariant

DOI: 10.3233/JCM-2002-21-207

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 2, no. 1-2, pp. 51-56, 2002