Search for 2-D Solitons in Gross–Pitaevskii Equation
- 83 Downloads
The article proposes an iterative method to find soliton solutions of the two-dimensional Gross-Pitaevskii equation. The method also finds soliton solutions of other nonlinear evolution equations. The method can be efficiently implemented on parallel computer systems, producing high-accuracy soliton solutions.
Keywordssoliton iterative method analytical solution convergence nonlinear differential equation
Unable to display preview. Download preview PDF.
- 1.V. A. Trofimov and A. V. Rozantsev, “2D soliton formation of BEC at its interaction with external potential,” in: Proceedings of SPIE, 8497 (2012).Google Scholar
- 2.Yu. S. Kivshar and G. P. Agrawal, Optical Solitons [Russian translation], Fizmatlit (2005).Google Scholar
- 3.E. B. Tereshin, V. A. Trofimov, and M. V. Fedotov, “Conservative finite difference scheme for the problem of propagation of a femtosecond pulse in a nonlinear photonic crystal with non-reflecting boundary conditions,” Comput. Math. Mathematical Phys., 46, No. 1, 154–164 (2006).CrossRefMathSciNetGoogle Scholar
- 4.V. S. Laponin, N. P. Savenkova, and V. P. Il’yutko, “A numerical method to find soliton solutions,” Prikl. Mat. Informat., MGU, No. 38, 69–80 (2011).Google Scholar
- 5.A. Newell, Solitons in Mathematics and Physics [Russian translation], Mir, Nauka (1989).Google Scholar
- 6.V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Soliton Theory: The Inverse Problem Method [in Russian], Nauka, Moscow (1980).Google Scholar