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Nonlinear Schrödinger equation with variable coefficients: Concentrated solution and its breakdown

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Abstract

The nonlinear Schrödinger equation with variable coefficients is applied to a description of wave processes in inhomogeneous media. The Cauchy problem is considered with initial data from the Schwartz class. Conditions of the conservation of a concentrated solution for all values of time are developed based on the study of the local solvability of this problem. The possibility of the concentrated solution breaking down within a finite period of time is discussed.

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Authors
  1. M. A. Bisyarin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 173, pp. 42–47, 1988.

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Bisyarin, M.A. Nonlinear Schrödinger equation with variable coefficients: Concentrated solution and its breakdown. J Math Sci 55, 1672–1676 (1991). https://doi.org/10.1007/BF01098205

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  • DOI: https://doi.org/10.1007/BF01098205

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