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Integrable nonlinear equations on a half-axis

Abstract

A study is made of the nonlinear Schrödinger equation and the modified Kortewegde Vries equation on the half-axis 0≤x<∞. Classes of solutions are identified when there is sufficient initial data for unique solvability of a corresponding problem. The class of solutions investigated is characterized in terms of the Weyl-Titchmarsh function of an auxiliary linear problem. A solution is constructed in explicit form when the corresponding Weyl-Titchmarsh function v(t, z) is a rational function of z.

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1578–1584, November, 1991.

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Sakhnovich, L.A. Integrable nonlinear equations on a half-axis. Ukr Math J 43, 1470–1476 (1991). https://doi.org/10.1007/BF01067289

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Keywords

  • Initial Data
  • Rational Function
  • Nonlinear Equation
  • Explicit Form
  • Linear Problem