Physics, mathematics, and technology

2012 Issue №4

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Nonlinear dissipative structures as model of two-dimensional optic solitons



We study the Darboux and Laplace transformations for the Boiti — Leon — Pempinelli equations (BLP). These equations are the (1+2) generalization of the sinh-Gordon equation. In addition, the BLP equations reduced to the Burgers equation in a one-dimensional limit. Localized nonsingular solutions in both spatial dimensions and anti ”blow-up” solutions are constructed.


1. Boiti M., Leon J. J.-P., Pempinelli F. Spectral transform for a two spatial dimension extension of the dispersive long wave equation // Inverse  Problems. 1987. Vol. 3. P. 371.
2. Гарагаш Т. И. О модификации теста Пенлеве для систем нелинейных дифференциальных уравнений в частных производных // ТМФ. 1994. Т. 100, № 3. С. 367—376.
3. Юров А. В. Сопряженные цепочки дискретных симметрий (1+2) нелинейных уравнений // ТМФ. 1999. Т. 119, № 3. С. 419–428.