In present report the algorithm for solving 4-waves dispersive equation are proposed. We consider both asymmetric and symmetric cases. The set of asymmetric.

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In present report the algorithm for solving 4-waves dispersive equation are proposed. We consider both asymmetric and symmetric cases. The set of asymmetric solutions is generated by effective algorithm, and the set of symmetric solutions is described as the solutions series defined parametrically. E. Каrtashova (RISC, J. Kepler University, Linz, Austria) М. Lvov (RIIT, Kherson State University, Kherson, Ukraine) Effective Algorithm for Full Solution of Dispersive Equation for 4-waves Nonlinear Resonances

Problems Definition Given: (1) (2) (3) Find: All satisfies (1)-(3) Let The system of equations for the problem:

1. Elena Kartashova. Fast Computation Algorithm for Discrete Resonances among Gravity Waves. Journal of Low Temperature Physics, Vol. 145, Nos. 1–4, November Elena Kartashova, Alexey Kartashov. LaminatedWave Turbulence: Generic Algorithms I. International Journal of Modern Physics C, Vol. 17, No. 11 (2006), Elena Kartashova, Alexey Kartashov. LaminatedWave Turbulence: Generic Algorithms II. Communications in computational physics. Vol. 2, no. 4, pp Elena Kartashova, Guenther Mayrhofer. Cluster formation in mesoscopic systems. Physica A 385 (2007) 527– Elena Kartashova, Sergey Nazarenko, Oleksii Rudenko. Resonant interactions of nonlinear water waves in a finite basin. Physical review e 78, _2008_ Previous Publications

1.Все симметричные решения – серии (21)-(31) – частные случаи серии (39). Все эти серии генерируют прямоугольники. 2. Серия (20) – самая большая – генерирует параллелограммы. Она не выражается через (39). Таким образом, существуют симметричные решения, относящиеся к случаю (7) но не относящиеся к случаю (8) 3.Свойство симметричности решения может быть выражено в терминах равенства норм волновых векторов. Cуществуют асимметричные решения, в которых нормы пары векторов равны (случай 2b). Conclusion