The short pulse equation is integrable

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August undefined, 2024

WebOct 1, 2016 · The first integrable case is the original SPE, while the second one is a new equation which we have called the single-cycle pulse equation (SCPE) due to properties of its solutions. The SPE and the SCPE are two different “avatars” of one and the same sine-Gordon equation.

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WebApr 14, 2024 · When you add the bearish S&P500--RSI_14 divergence to the equation, it looks all set for a short-term bearish control to retest the 4000 psychological price at least. WebJun 1, 2006 · The short pulse equa tion is integrable. J. Phys. Soc. Jpn. 74 (2005) 239–241; nlin.SI/0409034. ... Short pulse equation (SPE) is a non-linear PDE, used in optical fibers, computer graphics, and ... hippodrome new york history

The Short Pulse Equation Is Integrable - NASA/ADS

WebAug 10, 2016 · Download PDF Abstract: In this paper, we analyze the long-time behavior of the solution of the initial value problem (IVP) for the short pulse (SP) equation. As the SP equation is a complete integrable system, which posses a Wadati-Konno-Ichikawa (WKI)-type Lax pair, we formulate a $2\times 2$ matrix Riemann-Hilbert problem to this IVP by … WebThis is a review of fiber-optic soliton propagation and of methods to determine the soliton content in a pulse, group of pulses or a similar structure. Of central importance is the … WebOct 1, 2016 · The short pulse equation is able to describe ultra short pulse, which plays a crucial part in the field of optical fiber propagation. In this paper, we investigate a … homes for sale in 15045

The short pulse equation is integrable - arXiv

The interaction solitons for the complex short pulse equation

WebThis model results in a set of diﬀerential equations that are coupled with the equation of motion for the rotating mass and with the equation of motion for the projectile. ... Investigation is carried out towards various UWB pulse candidates for Ultra-wideband Short-Range Radar Human ID System. Simulation results by Matlab for candidates of ... WebSep 17, 2024 · Integrable self-adaptive moving mesh schemes for short pulse type equations (the short pulse equation, the coupled short pulse equation, and the complex … hippodrome new yorkWebJun 1, 2024 · The complex short pulse (CSP) equation u x t = u + 1 2 ( u 2 u x) x is one of the most interesting and exotic nonlinear integrable equations, which was discovered very recently by Feng [13], [14]. In Eq. (2), u = u ( x, t) is a complex-valued function, representing the magnitude of the electric field, the subscripts t and x denote partial ... homes for sale in 15017 zip code

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The short pulse equation is integrable

Inverse scattering transform of a new optical short pulse system

WebJun 5, 2013 · In the second part of the talk, we construct integrable semi-discrete analogue of the complex short pulse equation by Hirota’s bilinear method and provide its multi-soliton solution. Finally, we show that this integrable discretization can be successfully used as a self-adaptive moving mesh method for the numerical simulation of the CSPE. WebAbstract A Bäcklund transformation (BT), which involves both independent and dependent variables, is established and studied for the short pulse (SP) equation. Based it, the nonlinear superposition... The short pulse equation: Bäcklund transformations and applications - Mao - 2024 - Studies in Applied Mathematics - Wiley Online Library

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Webmedia. They derived the short pulse (SP) equation uxt = u+ 1 6 u3 xx. (1) Chung et al [2] showed numerically that the SP equation provides a better approximation to the solution … WebFeb 4, 2010 · In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and …

WebOct 1, 2024 · The main purpose of this paper is to show that for the integrable Short Pulse (SP) equation u x t = u + 1 6 (u 3) x x or u t = (∂ − 1 u) + 1 2 u 2 u x, a super extension does … WebApr 12, 2024 · We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external potential, which …

WebMay 30, 2024 · The study of the integrability of the SP equation via a bi-Hamiltonian formalism [ 9, 10] has led naturally to define a hierarchy of commuting flows: the SP equation is the first positive flow while the EB equation is the first negative flow. Let us now obtain some possible nonlocal reductions of the system ( 9) and ( 11 ). WebSep 19, 2004 · The Short Pulse Equation Is Integrable. We prove that the Schafer–Wayne short pulse equation (SPE), which describes the propagation of ultrashort optical pulses …

WebSep 19, 2004 · The short pulse equation is integrable. We prove that the Schafer-Wayne short pulse equation (SPE) which describes the propagation of ultra-short optical pulses …

WebJun 4, 2013 · Bilinearizations to the Camassa-Holm equation,Degasperis-Procesi equation and their short-wave models ... (DP) equation and their short-wave limits (the Hunter-Saxton and the reduced Ostrovsky equations), the short pulse and coupled short equations etc. These equations share some common features: (1) they are connected to other known … homes for sale in 14618WebWe prove that the Schäfer-Wayne short pulse equation (SPE), which describes the propagation of ultrashort optical pulses in nonlinear media, is integrable. First, we discover a Lax pair of the SPE that is found to be of the Wadati-Konno-Ichikawa type. hippodrome norfolkWebSakovich, Sergei We prove that the Schäfer-Wayne short pulse equation (SPE), which describes the propagation of ultrashort optical pulses in nonlinear media, is integrable. … homes for sale in 14456WebBased on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short … homes for sale in 15108 area code paWebFeb 1, 2024 · The short pulse (SP) equation is an integrable equation. Multi-component generalizations of the SP equation are important for describing the polarization or anisotropic effects in optical fibers. An integrable semi-discretization of multi-component SP equation via Lax pair and Darboux transformation (DT) has been presented. ... homes for sale in 14221 zip codeWebBy means of transformations to nonlinear Klein-Gordon equations, we show that a generalized short pulse equation is integrable in two (and, most probably, only two) … hippodrome northamptonWebJul 25, 2024 · We consider three novel PDEs associated with the integrable generalizations of the short pulse equation classified recently by Hone {\\it et al} (2024 {\\it Lett. Math. Phys.} {\\bf 108} 927-947). In particular, we obtain a variety of exact solutions by means of a direct method analogous to that used for solving the short pulse equation. The main … homes for sale in 14850 zip code