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A Korteweg–DeVries type model for helical soliton solutions for quantum and continuum phenomena

Author

Listed:
  • Sergio Manzetti

    (Fjordforsk A/S, Midtun, Vangsnes 6894, Norway†Uppsala University, BMC, Dept Mol. Cell Biol, Box 596, Uppsala SE-75124, Sweden)

  • Alexander Trounev

    (#x2020;Uppsala University, BMC, Dept Mol. Cell Biol, Box 596, Uppsala SE-75124, Sweden‡A & E Trounev IT Consulting, Toronto, Canada)

Abstract

Quantum mechanical states are normally described by the Schrödinger equation, which generates real eigenvalues and quantizable solutions which form a basis for the estimation of quantum mechanical observables, such as momentum and kinetic energy. Studying transition in the realm of quantum physics and continuum physics is however more difficult and requires different models. We present here a new equation which bears similarities to the Korteweg–DeVries (KdV) equation and we generate a description of transitions in physics. We describe here the two- and three-dimensional form of the KdV like model dependent on the Plank constant ℏ and generate soliton solutions. The results suggest that transitions are represented by soliton solutions which arrange in a spiral-fashion. By helicity, we propose a conserved pattern of transition at all levels of physics, from quantum physics to macroscopic continuum physics.

Suggested Citation

  • Sergio Manzetti & Alexander Trounev, 2021. "A Korteweg–DeVries type model for helical soliton solutions for quantum and continuum phenomena," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-14, March.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:03:n:s0129183121500315
    DOI: 10.1142/S0129183121500315
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