Lattice and q-difference Darboux-Zakharov-Manakov systems via $\bar{\partial}$-dressing method

B.G. Konopelchenko (Dipartimento di Fisica dell'Universit\`a; Italy); Landau Institute for Theoretical Physics; Lecce; L.V. Bogdanov (IINS; Russia)

arxiv: solv-int/9501007 · v1 · pith:JPIDBX77new · submitted 1995-01-28 · solv-int · math.QA· nlin.SI· q-alg

Lattice and q-difference Darboux-Zakharov-Manakov systems via bar{partial}-dressing method

L.V. Bogdanov (IINS , Landau Institute for Theoretical Physics , Russia) , B.G. Konopelchenko (Dipartimento di Fisica dell'Universit\`a , Lecce , Italy) This is my paper

classification solv-int math.QAnlin.SIq-alg

keywords latticeq-differencesystemsdarboux-zakharov-manakovdressingmethodpartialscheme

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A general scheme is proposed for introduction of lattice and q-difference variables to integrable hierarchies in frame of $\bar{\partial}$-dressing method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov systems of equations are derived. Darboux, B\"acklund and Combescure transformations and exact solutions for these systems are studied.

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Lattice and q-difference Darboux-Zakharov-Manakov systems via bar{partial}-dressing method

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