I. T. Habibullin, “Sine-Gordon equation on the semi-axis”, TMF, 114:1 (1998), 115–125; Theoret. and Math. Phys., 114:1 (1998), 90

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Teoreticheskaya i Matematicheskaya Fizika, 1998, Volume 114, Number 1, Pages 115–125
DOI: https://doi.org/10.4213/tmf832 (Mi tmf832)

This article is cited in 10 scientific papers (total in 10 papers)

Sine-Gordon equation on the semi-axis

I. T. Habibullin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Full-text PDF (235 kB) Citations (10)

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DOI: https://doi.org/10.4213/tmf832

Abstract: We investigate the sine-Gordon equation

u_{t t} - u_{x x} + \sin u = 0

$u_{tt}-u_{xx}+\sin u=0$ on the semi-axis

x > 0

$x>0$ . We show that boundary conditions of the forms

u_{x} (0, t) = c_{1} \cos (u (0, t) / 2) + c_{2} \sin (u (0, t) / 2)

$u_x(0,t)=c_1\cos(u(0,t)/2)+ c_2\sin(u(0,t)/2)$ and

u (0, t) = c

$u(0,t)=c$ are compatible with the Bдcklund transformation. We construct a multisoliton solution satisfying these boundary conditions.

Received: 11.08.1997

English version:
Theoretical and Mathematical Physics, 1998, Volume 114, Issue 1, Pages 90–98
DOI: https://doi.org/10.1007/BF02557111

Bibliographic databases:

Language: Russian

Citation: I. T. Habibullin, “Sine-Gordon equation on the semi-axis”, TMF, 114:1 (1998), 115–125; Theoret. and Math. Phys., 114:1 (1998), 90–98

Citation in format AMSBIB

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\paper Sine-Gordon equation on the semi-axis

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\transl

\jour Theoret. and Math. Phys.

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\issue 1

\pages 90--98

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Linking options:

https://www.mathnet.ru/eng/tmf832

https://doi.org/10.4213/tmf832

https://www.mathnet.ru/eng/tmf/v114/i1/p115

This publication is cited in the following 10 articles:

Dubrovsky V.G. Topovsky V A., “Multi-Soliton Solutions of Kp Equation With Integrable Boundary Via Partial Differential -Dressing Method”, Physica D, 428 (2021), 133025
Dubrovsky V.G. Topovsky V A., “Multi-Lump Solutions of Kp Equation With Integrable Boundary Via Partial Derivative-Dressing Method”, Physica D, 414 (2020), 132740
Lima F.C., Simas F.C., Nobrega K.Z., Gomes A.R., “Boundary Scattering in the Phi(6) Model”, J. High Energy Phys., 2019, no. 10, 147
Aguirre A.R. Gomes J.F. Ymai L.H. Zimerman A.H., “N=1 Super Sinh-Gordon Model in the Half Line: Breather Solutions”, J. High Energy Phys., 2013, no. 4, 136
Corrigan E. Zambon C., “Infinite Dimension Reflection Matrices in the sine-Gordon Model with a Boundary”, J. High Energy Phys., 2012, no. 6, 050
Shamsutdinov, MA, “Dynamics of magnetic kinks in exchange-coupled ferromagnetic layers”, Physics of Metals and Metallography, 108:4 (2009), 327
Kundu, A, “Changing Solitons in Classical & Quantum Integrable Defect and Variable Mass sine-Gordon Model”, Journal of Nonlinear Mathematical Physics, 15 (2008), 237
Habibullin, I, “Quantum and classical integrable sine-Gordon model with defect”, Nuclear Physics B, 795:3 (2008), 549
A. Kundu, “Yang–Baxter algebra and generation of quantum integrable models”, Theoret. and Math. Phys., 151:3 (2007), 831–842
V. L. Vereshchagin, “Soliton solutions of an integrable boundary problem on the half-line for the discrete Toda chain”, Theoret. and Math. Phys., 148:3 (2006), 1199–1209

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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