Partial Solution-preserving Integrable generalization Method for Autonomous ODE Systems
DOI:
https://doi.org/10.47611/jsrhs.v11i3.2654Keywords:
mathematical modeling, ODE systems, integrabilityAbstract
In this paper, we propose a method for the generalization of some generic fundamental, abstract differential equations into generalized systems. We hypothesize that these generalized systems are fit to model some real-life phenomena, which can be of practical interest. We confirm our hypothesis by considering examples that are known to be confirmed with the experiment as well as examples that are still to be discovered.
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References or Bibliography
Allen, L and J. Eberly. Optical Resonance and Two-Levels Atoms. New York: Wiley, 1975.
AMOS, N. "The Rayleigh-van der Pol harmonic oscillator." International Journal of Electronics 43.6 (1977): 609-614.
Bailin, D. and A. Love. Introduction to Gauge Field Theory. Taylor & Francis, 1993.
Belmonte, A., H. Eisenberg and E. Moses. " From flutter to tumble: Inertial drag and froude similarity infalling paper ." Phys. Rev. Lett. (1998): 345-348.
Bender, C.M. and S.A. Orszag. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory. Springe, 1999.
Boulite, S., S Hadd and L and Maniar. "Feedback theory to the well-posedness of evolution equations ." Phil. Trans. R. Soc. A. (2020): 378.
Boyd, R.W. (2008). Nonlinear Optics, 3rd edition
Buldakov, N, et al. "Simulation of communication in the "heart-vessels" system." (2013).
Bullough, R., et al. "A general theory of self-induced transparency." Optical and Quantum Electronics (1974): 121-140.
Costabile, G. and R., Parmentier. "Analytic solution for fluxon propagation on Josephson junction with bias and loss." Low Temperature Physics-LT14 (1975): 112.
Joshi, S, S Sen and I Kar. "Synchronization of Coupled Oscillator Dynamics." IFAC (2016): 320-325.
McCall, S and E. Hahn. " Self-induced transparency by pulsed coherent light." Phys. Rev. Lett. (1967): 908-911.
Ming, C. "Solution of Differential Equations with Applications to." Dynamical Systems - Analytical and Computational Techniques. Intech, 2017. 233.
Newell, A. " CBNS." (1985): 43.
Pedersen, N. and K. Saermark. " Analytical solution for a Josephson-Junction model with capacitance,." (1973): 572-578. 69.
Trench, W. Elementary differential equations. Brooks-Cole Thomson Learning, 2013.
Zill, G. A First Course in Differential Equations with Modeling Applications. Cengage Learning., 2018.
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