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Solitons in Optical Metamaterials with Trial Solution Approach and Bäcklund Transform of Riccati Equation

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This paper obtains soliton solutions in optical metamaterials. There are a couple of integration techniques that are applied to the nonlinear Schrödinger’s equation, with full nonlinearity, that serves as the governing model. These are trial solution approach and application of Bäcklund transform to Riccati equation. There are four types of nonlinear media that are studied in this paper. They are Kerr law that is also referred to as cubic law, power law, parabolic law occasionally referred to as cubic-quintic law and finally dual-power law nonlinearity. Bright, dark and singular soliton solutions are obtained in optical metamaterials with the aid of the two algorithms. As a byproduct of these two approaches, singular periodic solutions and plane wave solutions are also listed although these are not utilized in optical metamaterials. There are several constraint conditions that naturally fall out from the solution structure. These conditions guarantee the existence of these variety of solutions.
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Keywords: Integrability; Metamaterials; Solitons

Document Type: Research Article

Affiliations: 1: Department of Engineering Mathematics and Physics, Higher Institute of Engineering El Shorouk, Egypt 2: Department of Engineering Sciences, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran 3: Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa 4: Centre for Applied Physics, Central University of Jharkhand, Brambe, Ranchi 835205, India 5: School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan-430212, People’s Republic of China 6: Department of Mathematics, Howard University, Washington, DC-20059, USA 7: Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA 8: Science Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Publication date: December 1, 2015

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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