The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy - Nonlinear Sciences > Exactly Solvable and Integrable SystemsReportar como inadecuado




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Abstract: We discuss the algebro-geometric initial value problem for the Ablowitz-Ladikhierarchy with complex-valued initial data and prove unique solvabilityglobally in time for a set of initial Dirichlet divisor data of full measure.To this effect we develop a new algorithm for constructing stationarycomplex-valued algebro-geometric solutions of the Ablowitz-Ladik hierarchy,which is of independent interest as it solves the inverse algebro-geometricspectral problem for general non-unitary Ablowitz-Ladik Lax operators,starting from a suitably chosen set of initial divisors of full measure.Combined with an appropriate first-order system of differential equations withrespect to time a substitute for the well-known Dubrovin-type equations, thisyields the construction of global algebro-geometric solutions of thetime-dependent Ablowitz-Ladik hierarchy.The treatment of general non-unitary Lax operators associated with generalcoefficients for the Ablowitz-Ladik hierarchy poses a variety of difficultiesthat, to the best of our knowledge, are successfully overcome here for thefirst time. Our approach is not confined to the Ablowitz-Ladik hierarchy butapplies generally to 1+1-dimensional completely integrable soliton equationsof differential-difference type.



Autor: F. Gesztesy, H. Holden, J. Michor, G. Teschl

Fuente: https://arxiv.org/







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