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On Complex-Valued Solutions of the General Loaded Korteweg–de Vries Equation with a Source

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Abstract

Using the inverse scattering method, we derive the evolution of the scattering data of a nonself-adjoint Sturm–Liouville operator whose potential is a solution of the general loaded Korteweg–de Vries equation with a self-consistent source in the class of rapidly decaying complex-valued functions. An example is given to illustrate the application of the results obtained.

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Authors and Affiliations

  1. Samarkand State University, Samarkand, 140104, Uzbekistan

    A. B. Khasanov

  2. Khwarazm Branch of Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Urgench, Uzbekistan

    U. A. Hoitmetov

  3. Urgench State University, Urgench, 220100, Uzbekistan

    U. A. Hoitmetov

Authors
  1. A. B. Khasanov
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  2. U. A. Hoitmetov
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Correspondence to A. B. Khasanov or U. A. Hoitmetov.

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Translated by V. Potapchouck

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Khasanov, A.B., Hoitmetov, U.A. On Complex-Valued Solutions of the General Loaded Korteweg–de Vries Equation with a Source. Diff Equat 58, 381–391 (2022). https://doi.org/10.1134/S0012266122030089

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  • DOI: https://doi.org/10.1134/S0012266122030089

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