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Article information
2017 , Volume 22, ¹ 5, p.3-13
Bulygin A.D., Zemlyanov A.A.
Fully conservative numerical scheme for nonlinear Schrodinger equation with higher nonlinearities
The paper examines the performance conditions to satisfy the complete conservatism property for most widely used various numerical schemes in the context of filamentation problem of the nonlinear Schrodinger equation (NLSE). Stationary radial model has two integrals of motion which are the Hamilton function and the “number of particles”. We set the explicit form of the unbalanced terms arising in asymmetrical schemes of splitting into physical factors. On the basis of numerical calculations it is understood that the standard scheme constructing the adaptive meshes with filamentation leads to a catastrophic violation of the conservation laws. We found the conditions for the numerical mesh for which it is possible to satisfy the conservation law with any acceptable accuracy for both fully symmetric scheme and the scheme with splitting on physical factors that includes the Crank -Nicolson scheme.
[full text]
Keywords: filamentation, nonlinear Schrodinger equation, conservation laws, fully conservative scheme
Author(s):
Bulygin Andrey Dmitrievich
PhD.
Position: Research Scientist
Office: V.E. Zuev Institute of Atmospheric Optics SB RAS
Address: 634055, Russia, Tomsk, 1, Academician Zuev square
E-mail: b.a.d@iao.ru
Zemlyanov Aleksandr Anatol`evich
Dr.
Position: Head of Laboratory
Office: V.E. Zuev Institute of Atmospheric Optics SB RAS
Address: 634055, Russia, Tomsk, 1, Academician Zuev square
E-mail: zaa@iao.ru
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Bibliography link:
Bulygin A.D., Zemlyanov A.A. Fully conservative numerical scheme for nonlinear Schrodinger equation with higher nonlinearities // Computational technologies. 2017. V. 22. ¹ 5. P. 3-13
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