Coupled modified complex short pulse equationBinary Darboux transformationBright–dark solitonAsymptotic behaviorThe short pulse equation is an important integrable equation in nonlinear optical fibers, which describes the propagation of ultra-short optical pulses in nonlinear media. Popowicz proposed the ...
WestudyanewhierarchyofequationscontainingtheShortPulseequation,whichdescribesthe evolutionofveryshortpulsesinnonlinearmedia,andtheElasticBeamequation,whichdescribes nonlineartransverseoscillationsofelasticbeamsundertension.Weshowthatthehierarchyof equationsisintegrable.WeobtainthetwocompatibleHamiltonianstructures.Weconstructan...
Integrable semi-discretization of a multi-component short pulse equation, accepted by J. Math. Phys. 2015;56:043502.Feng B. F., Maruno K., Ohta Y., Integrable semi-discretizations of the reduced Ostrovsky equation. J. Phys. A: Math. Theo., 48(2015), 135203....
The short pulse equation (SPE) is considered as an initial-boundary value problem. It is found that the solutions of the SPE must satisfy an integral relation otherwise the temporal derivative exhibits discontinuities. This integral relation is not necessary for a solution to exist. An infinite nu...
The paper aims at developing the Riemann–Hilbert (RH) approach for the modified Camassa–Holm (mCH) equation on the line with non-zero boundary conditions, in the case when the solution is assumed to approach two different constants at different sides of the line. We present detailed propertie...
The short pulse equation by a Riemann–Hilbert approach 2017, Letters in Mathematical Physics A Riemann-Hilbert approach for the Degasperis-Procesi equation 2013, Nonlinearity Multi-component generalizations of the CH equation:Geometrical aspects, peakons and numerical ex...
A note on loop-soliton solutions of the short-pulse equation Phys. Lett. A, 374 (2010), pp. 4321-4323 View PDFView articleView in ScopusGoogle Scholar [30] Rogers C., Schief W.K., Szereszewski A. Loop soliton interaction in an integrable nonlinear telegraphy model: reciprocal and Backl...
The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. ...
equation, which paves a way for the construction of integrable discretizations of these soliton equations. In addition, it can be observed that a deformed negative flow exists and is compatible with the regular negative and positive flows. An extension of KP theory is called for to explain this...
They proposed the following integrable model,iqt+(q1+|q|2)xx=0, which is later called the Wadati-Konno-Ichikawa (WKI) equation. Then, Wadati, Konno and Ichikawa did a series of work on WKI equation, including the infinite number of conservation laws and an application that it can be ...