Analytical Solutions of Undamped and Autonomous Cubic-Quintic Duffing Equation
Serge Bruno Yamgoué,
Jules Hilaire Kamga
Issue:
Volume 3, Issue 5, September 2015
Pages:
159-165
Received:
8 July 2015
Accepted:
16 July 2015
Published:
25 July 2015
Abstract: In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The conditions of existence of these solutions which also represent solitons of some wave equations are carefully analyzed.
Abstract: In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The co...
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Einstein: Unification Theory and Unification of Basic Forces-II
M. Tajuddin,
Md. Haider Ali Biswas
Issue:
Volume 3, Issue 5, September 2015
Pages:
166-177
Received:
15 July 2015
Accepted:
27 July 2015
Published:
14 August 2015
Abstract: Unification theory is ‘a complete unified theory that will describe everything in the universe’ (Hawking, 1996). Unification theory is expressed through spherical geometry and ‘all dimensional geometry is included in spherical geometry. Thus spherical geometry in the form of unification theory describes all the laws of the universe’ (Tajuddin and Biswas, 2015). This theory has enough proofs and supports in favor of its formation and working capacity. The unification theory and spherical geometry are not any type of utopian ideas but they are basic and real concepts of the world that are searched by our scientists for the last hundred of years. Actually this unification theory is the Grand Unified Theory (GUT) of four basic forces of physical sciences, and spherical geometry is the supreme geometry that covers the unified force. These two concepts are related to each other and discussed here (vide: Different sections of the article)
Abstract: Unification theory is ‘a complete unified theory that will describe everything in the universe’ (Hawking, 1996). Unification theory is expressed through spherical geometry and ‘all dimensional geometry is included in spherical geometry. Thus spherical geometry in the form of unification theory describes all the laws of the universe’ (Tajuddin and B...
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The Unification of Mass and Energy
Issue:
Volume 3, Issue 5, September 2015
Pages:
178-182
Received:
23 July 2015
Accepted:
3 August 2015
Published:
14 August 2015
Abstract: Our universe is an amazing place where matter floats. The endless stories about changing of mass or energy in the universe may overwhelm all tabloid writers. However, Einstein found a very simple way to cover all the stories in “One” equation: E=MC2. Yes, the “C” actually stands for speed of light (photon) in the vacuum. Few will argue photons are electromagnetic/radiation power. However, many deny photon’s mass status. In this paper, the author will assure you that photon is mass, which also happens to serve the foundation for all gravitational power/positional energy that exists today after a big bang. ⑴ Furthermore, the author will also assure you that neutrino is the dark matter that floats in the space chilling with electrons (- and +). Again, the author assures you that the famous gamma ray burst is just cosmic-sized of our well-studied experiment in our lab: e- + e+ → γ + γ! Our current universe’s mass and energy (detectable or undetectable) are all derived from a big bang’s photons. The primary objective of this study is to uncover the unified origin for both mass and energy in the universe along with their evolutionary path in the discipline of Newtonian physics.
Abstract: Our universe is an amazing place where matter floats. The endless stories about changing of mass or energy in the universe may overwhelm all tabloid writers. However, Einstein found a very simple way to cover all the stories in “One” equation: E=MC2. Yes, the “C” actually stands for speed of light (photon) in the vacuum. Few will argue photons are ...
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