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Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2016

Mathematics

Publications

Embry-Riddle Aeronautical University

Articles 1 - 6 of 6

Full-Text Articles in Physical Sciences and Mathematics

Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, S.C. Mancas Sep 2016

Ermakov Equation And Camassa-Holm Waves, Haret C. Rosu, S.C. Mancas

Publications

From the works of authors of this article, it is known that the solution of the Ermakov equation is an important ingredient in the spectral problem of the Camassa-Holm equation. Here, we review this interesting issue and consider in addition more features of the Ermakov equation which have an impact on the behavior of the shallow water waves as described by the Camassa-Holm equation.

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Integrable Abel Equations And Vein's Abel Equation, S.C. Mancas, Haret C. Rosu Apr 2016

Integrable Abel Equations And Vein's Abel Equation, S.C. Mancas, Haret C. Rosu

Publications

We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein’s Abel equation whose solutions are expressed in terms of the third order hyperbolic functions and a phase space analysis of the corresponding nonlinear oscillator is also provided.

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Nongauge Bright Soliton Of The Nonlinear Schrodinger (Nls) Equation And A Family Of Generalized Nls Equations, M. A. Reyes, D. Gutierrez-Ruiz, S. C. Mancas, H. C. Rosu Jan 2016

Nongauge Bright Soliton Of The Nonlinear Schrodinger (Nls) Equation And A Family Of Generalized Nls Equations, M. A. Reyes, D. Gutierrez-Ruiz, S. C. Mancas, H. C. Rosu

Publications

We present an approach to the bright soliton solution of the nonlinear Schrödinger (NLS) equation from the standpoint of introducing a constant potential term in the equation. We discuss a “nongauge” bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sechpsechp solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg–de Vries (KdV) and Benjamin–Bona–Mahony (BBM) equations when p=2.

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Existence Of Periodic Orbits In Nonlinear Oscillators Of Emden-Fowler Form, S.C. Mancas, Haret C. Rosu Jan 2016

Existence Of Periodic Orbits In Nonlinear Oscillators Of Emden-Fowler Form, S.C. Mancas, Haret C. Rosu

Publications

The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows …

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A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya Jan 2016

A Note On Vector Valued Discrete Schrödinger Operators, Keshav R. Acharya

Publications

The main purpose of this paper is to extend some theory of Schrödinger operators from one dimension to higher dimension. In particular, we will give systematic operator theoretic analysis for the Schrödinger equations in multidimensional space. To this end, we will provide the detail proves of some basic results that are necessary for further studies in these areas. In addition, we will introduce Titchmarsh- Weyl m− function of these equations and express m− function in term of the resolvent operators.

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Remling's Theorem On Canonical Systems, Keshav R. Acharya Jan 2016

Remling's Theorem On Canonical Systems, Keshav R. Acharya

Publications

In this paper, we extend the Remling’s Theorem on canonical systems that the ω limit points of the Hamiltonian under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure of a canonical system.

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