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An analytical study for (2 + 1)-dimensional Schrödinger equation.

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The homotopy analysis method effectively solves (2+1)-dimensional Schrödinger equations, offering an alternative to traditional techniques. Its results closely match exact solutions, validating its applicability.

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Area of Science:

  • Mathematical Physics
  • Nonlinear Dynamics

Background:

  • Schrödinger equations are fundamental in quantum mechanics and nonlinear optics.
  • Existing analytical methods often rely on approximations or small parameters.

Purpose of the Study:

  • To apply the homotopy analysis method (HAM) for solving (2+1)-dimensional Schrödinger equations.
  • To demonstrate HAM as a viable alternative to traditional methods, avoiding linearization and unrealistic assumptions.
  • To validate HAM by comparing its solutions with exact solutions for various forms of the equation.

Main Methods:

  • The homotopy analysis method (HAM) was employed.
  • The method was applied to diverse forms of (2+1)-dimensional Schrödinger equations.
  • Solutions obtained via HAM were rigorously compared against known exact solutions.

Main Results:

  • The homotopy analysis method successfully yielded solutions for the (2+1)-dimensional Schrödinger equations.
  • A strong agreement was observed between the HAM solutions and the exact solutions.
  • The method proved effective without requiring small parameters or linearization.

Conclusions:

  • The homotopy analysis method is a powerful and valid technique for solving complex nonlinear partial differential equations like the Schrödinger equation.
  • HAM provides a reliable and accurate alternative for researchers seeking non-perturbative analytical solutions.
  • The study confirms HAM's potential for broader applications in mathematical physics and nonlinear science.