Geometric Study of 2D-Wave Equations in View of K-Symbol Airy Functions
Abstract
:1. Introduction
2. Approaches
2.1. Normalized Airy Function
2.2. K-Symbol Calculus
2.3. K-Airy Differential Operator
2.4. Univalent Solution of the k-Wave Equation
3. Results and Discussion
- Solutions that are periodic exist because is an integer with Keobe function. Since individual modes do not necessarily have to be periodic, this restriction is not required. Instead, the value of t will be determined by the boundary conditions. Furthermore, it is asserted that without sacrificing generality, and special emphasis is given to solutions that behave as . The waves in the direction of positive t are attenuated in this way. The form of the waves traveling in the direction of negative t is the same (symmetric sense).
- The way in which the concept is developed here readily lends itself to many generalizations. This represents an intriguing situation when the height of the top border varies along the direction of propagation. The normalized analytic function is seen as a function of to obtain the normalized univalent solution in the complex model under study.
- It may be anticipated that a waveguide with slowly changing characteristics will not differ greatly from a waveguide with a constant cross-section based on fundamental principles. The structure of the modes may be used to identify a normalized waveguide with a univalent function. The ideal ground conductivity is now standardized to a value that is very near to unity.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Hadid, S.B.; Ibrahim, R.W. Geometric Study of 2D-Wave Equations in View of K-Symbol Airy Functions. Axioms 2022, 11, 590. https://doi.org/10.3390/axioms11110590
Hadid SB, Ibrahim RW. Geometric Study of 2D-Wave Equations in View of K-Symbol Airy Functions. Axioms. 2022; 11(11):590. https://doi.org/10.3390/axioms11110590
Chicago/Turabian StyleHadid, Samir B., and Rabha W. Ibrahim. 2022. "Geometric Study of 2D-Wave Equations in View of K-Symbol Airy Functions" Axioms 11, no. 11: 590. https://doi.org/10.3390/axioms11110590