Variational Principle of the Unstable Nonlinear Schrödinger Equation with Fractal Derivatives Article Swipe
Kang‐Jia Wang
,
Ming Li
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/axioms14050376
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/axioms14050376
The well-known nonlinear Schrödinger equation (NLSE) plays a crucial role in describing the temporal evolution of disturbances in marginally stable or unstable media. However, when the media is a fractal form, it becomes ineffective. Thus, the fractal modification to the NLSE is presented based on the fractal derivative in this work for the first time. The semi-inverse method is employed to establish the fractal variational principle. The entire process of deriving the fractal variational principle is presented in detail. To our knowledge, the fractal variational principle mentioned in this article is the first exploration and report to date. The fractal variational principle established in this paper is expected to deepen our understanding of the essence of physical phenomena in the fractal space and offer new ideas for the application and exploration of the variational approaches.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/axioms14050376
- https://www.mdpi.com/2075-1680/14/5/376/pdf?version=1747400500
- OA Status
- gold
- Cited By
- 10
- References
- 51
- Related Works
- 10
- OpenAlex ID
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https://openalex.org/W4410439834Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3390/axioms14050376Digital Object Identifier
- Title
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Variational Principle of the Unstable Nonlinear Schrödinger Equation with Fractal DerivativesWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-05-16Full publication date if available
- Authors
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Kang‐Jia Wang, Ming LiList of authors in order
- Landing page
-
https://doi.org/10.3390/axioms14050376Publisher landing page
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https://www.mdpi.com/2075-1680/14/5/376/pdf?version=1747400500Direct link to full text PDF
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goldOpen access status per OpenAlex
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https://www.mdpi.com/2075-1680/14/5/376/pdf?version=1747400500Direct OA link when available
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Fractal, Nonlinear system, Variational principle, Nonlinear Schrödinger equation, Mathematics, Mathematical analysis, Applied mathematics, Schrödinger equation, Classical mechanics, Mathematical physics, Physics, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
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10Total citation count in OpenAlex
- Citations by year (recent)
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2025: 10Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.employed | 59 |
| abstract_inverted_index.equation | 4 |
| abstract_inverted_index.expected | 107 |
| abstract_inverted_index.physical | 116 |
| abstract_inverted_index.temporal | 13 |
| abstract_inverted_index.unstable | 21 |
| abstract_inverted_index.establish | 61 |
| abstract_inverted_index.evolution | 14 |
| abstract_inverted_index.mentioned | 86 |
| abstract_inverted_index.nonlinear | 2 |
| abstract_inverted_index.phenomena | 117 |
| abstract_inverted_index.presented | 42, 76 |
| abstract_inverted_index.principle | 74, 85, 101 |
| abstract_inverted_index.derivative | 47 |
| abstract_inverted_index.describing | 11 |
| abstract_inverted_index.knowledge, | 81 |
| abstract_inverted_index.marginally | 18 |
| abstract_inverted_index.principle. | 65 |
| abstract_inverted_index.well-known | 1 |
| abstract_inverted_index.application | 128 |
| abstract_inverted_index.approaches. | 134 |
| abstract_inverted_index.established | 102 |
| abstract_inverted_index.exploration | 93, 130 |
| abstract_inverted_index.variational | 64, 73, 84, 100, 133 |
| abstract_inverted_index.Schrödinger | 3 |
| abstract_inverted_index.disturbances | 16 |
| abstract_inverted_index.ineffective. | 33 |
| abstract_inverted_index.modification | 37 |
| abstract_inverted_index.semi-inverse | 56 |
| abstract_inverted_index.understanding | 111 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 98 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.99499093 |
| citation_normalized_percentile.is_in_top_1_percent | True |
| citation_normalized_percentile.is_in_top_10_percent | True |