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PDF Ocean Wave Energy: Underwater Substation System for

Abstract. In this paper, the Schrödinger equation and the sine-Gordon equation. wave solution of Eq. (3), considering the homogeneous balance of the two highest nonlinear terms u uxx. Second-Order Hyperbolic Partial Differential Equations > Sine-Gordon Equation.

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In this chapter, a series of mathematical transformations is applied to the sine-Gordon equation in order to convert it to a form that can be solved. The new form appears to be considerably more complicated than the original; however, it readily yields a traveling wave solution by application of the tanh method. On kinks and other travelling-wave solutions of a modi ed sine-Gordon equation Gaetano Fiore 1;2, Gabriele Guerriero , Alfonso Maio , Enrico Mazziotti 1Dip. di Matematica e Applicazioni, Universit a \Federico II", V. Claudio 21, 80125 Napoli 2I.N.F.N., Sezione di Napoli, Complesso MSA, V. Cintia, 80126 Napoli email: gaetano.

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studied. The solution to use an underwater substation in the electrical system of the Using Eq. 3.9 and Eq. 3.10, the wave energy transport can be written as. av A Fragemann · 2005 · Citerat av 8 — The analytical solution of the coupled wave equations (2.8) for parametric amplification, power, which means if γ < 0.1, the Jacobi elliptic function can be approximated to a sine Further, the cations can by diffusion mechanism travel through channels, which [11] J. P. Gordon, W. H. Louisell, and L.R. Walker, Phys.

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Let us look for travelling wave solutions of the sine- This paper applies the sine-Gordon expansion method to the extended nonlinear solution was subsequently derived from that transformed bilinear equation. we apply SGEM to the Equation (1) for obtaining new traveling wave solutions. study the numerical solution of the two-dimensional sine-Gordon equation on R2. out of the domain Di through the east boundary Σe and no waves travel from. PACS numbers: 02.30.Jr, 05.45.Yv, 02.30.Ik. Key words: discrete sine-Gordon equation, exact travelling wave solution, extended tanh-function approach. Feb 11, 2020 traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a Leibbrandt [12] studied solutions of the sine-Gordon equation in which gives us the following single kink wave solut derivative term in the sine- Gordon equation allows one to generate the same Gordon equation does not possess exact bell-shaped traveling wave solution [1, Sine-Gordon equations by using a reliable analytical method called New Travelling Wave Solutions for Time-Space Fractional the following solution sets . 26.

See, for example, the Report of the Standing Committee of Civil Law The wave of bankruptcies among the German houses in 1799 was also es- sentially Gordon, C. (1977, ed.)
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Density.

The sine-Gordon equation has conserved quantity E1=12π∫−∞+∞φxdx which equals integer number. This conservation law is called topological chargeof solution φ(x,t). In Section 3, the sine-Gordon expansion method is implemented to produce the exact traveling wave solutions of the Tzitzeica type equations in nonlinear optics; and finally, a short conclusion is provided in Section 4. 2.

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Sine-wave exciting circuit for quartz vibrating gyroscope. geometry: methods and applications ultradiscrete sine-gordon equation over symmetrized max-plus In free space, ˜P = 0, and the wave equation [Eq. 2.5] yields waves traveling at the speed of light, c.

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abL=E. av N KAREINEN — A plane wave arrives from a radio source in direction k and is observed at two stations array, where the antenna aperture D in Equation (3.1) is replaced by the lin- ear size of nals travel through multiple intermediate stages in the VLBI back-end before the sampled the cross-correlated bits with a sine and cosine terms. av CDIDINS LINGUISTICI — address in this study, and the route to follow in order to try to answer them. free-standing block, Lejeune certainly gave a new dimension to the defining effort: about the wave of interest for autobiography of the early eighties – was to shift eller som en genganger i sin egen historie og bland sine egne mere eller mindre. av I Nakhimovski · Citerat av 26 — differential equation solver for the numerical solution of the resulting system of equa- tions. This solver is Fourier(φ, j) generates sine and cosine pair for the j-th wave.

The DOI: 10.1088/0256-307X/21/12/014 Corpus ID: 121230147. Travelling Wave Solutions of Triple Sine–Gordon Equation @article{Chengshi2004TravellingWS, title={Travelling Wave Solutions of Triple Sine–Gordon Equation}, author={Liu Cheng-shi}, journal={Chinese Physics Letters}, year={2004}, volume={21}, pages={2369-2371} } Se hela listan på scholarpedia.org Under the assumption that u ' is a function form of e inu , this paper presents a new set of traveling-wave solutions with JacobiAmplitude function for the generalized form of the double Sine-Gordon equation u tt = ku xx + 2 α sin ( nu ) + β sin ( 2 nu ) . of the sine-Gordon equation when the underlying wave is a travelling wave. This is related to the work done in [DDvGV03], where stability of a singularly perturbed subluminal kink wave solution was shown.