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Multidimensional solitons and their spectral transforms

1990; American Institute of Physics; Volume: 31; Issue: 11 Linguagem: Inglês

10.1063/1.529013

1527-2427

M. Boiti, Jean-François Léon, F. Pempinelli,

Advanced Fiber Laser Technologies

The soliton solution to the hierarchy of two-dimensional nonlinear evolution equations related to the Zakharov–Shabat spectral problem (including the Davey–Stewartson equation) are derived and studied. The solitons are localized two-dimensional structures traveling on straight lines at constant velocities. Their spectral transform is not uniquely defined and this point is discussed by giving two explicit different spectral transforms of the one-soliton solution and also by giving the general dependence of the spectral transform on the definition of the basic Jost-like solutions.