Abstract
A new method for constructing multidimensional nonlinear integrable systems and their solutions by means of a nonlocal Riemann problem is presented. This is the natural generalization of the method of the local Riemann problem to the case of several space variables and includes the well-known Zakharov-Shabat method of dressing by Volterra operators.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 77–91, 1984.
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Zakharov, V.E., Manakov, S.V. Multidimensional nonlinear integrable systems and methods for constructing their solutions. J Math Sci 31, 3307–3316 (1985). https://doi.org/10.1007/BF02107232
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DOI: https://doi.org/10.1007/BF02107232