On an ill-posed problem for system of coupled sinh-Gordon equations

Authors
  • Devendra Kumar

    Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India

  • Jagdev Singh

    Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India

Keywords:
ill-posed problem, Sinh-Gordon equation, regularization
Abstract

The aim of this paper is considering the initial value problem for a system of coupled nonlinear sinh-Gordon equations by the association between two regularization methods: filter and truncation Fourier. Firstly, we give an example to show that the problem does not satisfy the third property which is called ill-posed in the sense of Hadamard. Secondly, under some a priori assumptions, we propose the stable regularization methods to regularize the system, i.e. the corresponding regularized solution converge to the exact solution in \(L^2\)-norm. Finally, to illustrate the proposed efficiency in the theoretical part, we show some numerical tests to check the convergence of the regularized solution and the regularized errors.

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Additional Files
Published
28-03-2025
Section
Research Article
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Copyright (c) 2023 Devendra Kumar, Jagdev Singh

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

On an ill-posed problem for system of coupled sinh-Gordon equations. (2025). Letters on Applied and Pure Mathematics, 1(1), 43-54. https://doi.org/10.66147/lapm.20231115

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