On the Existence and Approximation of Solutions to a Nonlinear Schrodinger-Type Equation

Document Type : Research Article

Authors

1 Department of Physics, Prof. Rajendra Singh (Rajju Bhaiya) Institute of Physical Sciences for Study and Research, Veer Bahadur Singh Purvanchal University, Jaunpur, 222003, Uttar Pradesh, India

2 Department of Physics, Faculty of Science and Technology, JSPM University, Pune, 412207, Maharashtra, India

3 Department of Mathematics, Faculty of Engineering and Technology, Veer Bahadur Singh Purvanchal University, Jaunpur, 222003, Uttar Pradesh, India

Abstract

We investigate the mathematical structure and approximate solutions of a nonlinear equation arising in quantum mechanics. Specifically, we study a stationary nonlinear Schr\"odinger equation with a cubic nonlinearity, which is relevant in models of Bose--Einstein condensates and nonlinear optics. We establish existence results under suitable boundary conditions and develop a perturbative approximation scheme for small coupling. Numerical experiments illustrate the validity of the approximation and the emergence of localized states.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 10, Issue 2
December 2025
Pages 229-236

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History

  • Receive Date: 26 November 2025
  • Accept Date: 24 December 2025
  • Publish Date: 30 December 2025

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