Geodesic
The numerical algorithm construction for the vector Zakharov system with damping
Matematičeskoe modelirovanie, Tome 12 (2000) no. 11, pp. 102-114.

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The paper presents a new algorithm to solve the Zakharov system with damping. The numerical code based on the split-operator with respect to physical processes is suggested. The truncated Schrödinger equation included into the system, is used as a predictor on the first stage of a scheme step. It is shown that this predictor makes it possible to calculate the module of the solution on each step with enough accuracy. The phase correction is perfomed by the same operator exponential method using just determined module. The suggested method is illustrated through the example of turbulent solution of the system beyond the point of maximum, corresponding to the collapse situation in the system without damping. 
@article{MM_2000_12_11_a7,
     author = {A. D. Yunakovsky and \'E. M. Sher},
     title = {The numerical algorithm construction for the vector {Zakharov} system with damping},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {102--114},
     publisher = {mathdoc},
     volume = {12},
     number = {11},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2000_12_11_a7/}
}
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A. D. Yunakovsky; É. M. Sher. The numerical algorithm construction for the vector Zakharov system with damping. Matematičeskoe modelirovanie, Tome 12 (2000) no. 11, pp. 102-114. http://geodesic.mathdoc.fr/item/MM_2000_12_11_a7/