Hoitmetov, Umid On the Cauchy problem for the mKdV-sine-Gordon equation with an additional term. (English) Zbl 1516.35371 Acta Appl. Math. 184, Paper No. 7, 15 p. (2023). MSC: 35Q53 35P25 47A40 37K15 37K10 45P05 35R30 78A60 PDFBibTeX XMLCite \textit{U. Hoitmetov}, Acta Appl. Math. 184, Paper No. 7, 15 p. (2023; Zbl 1516.35371) Full Text: DOI
Uddin, M. Hafiz; Zaman, U. H. M.; Arefin, Mohammad Asif; Akbar, M. Ali Nonlinear dispersive wave propagation pattern in optical fiber system. (English) Zbl 1508.35203 Chaos Solitons Fractals 164, Article ID 112596, 10 p. (2022). MSC: 35R11 35Q53 35C08 35B06 78A60 26A33 PDFBibTeX XMLCite \textit{M. H. Uddin} et al., Chaos Solitons Fractals 164, Article ID 112596, 10 p. (2022; Zbl 1508.35203) Full Text: DOI
Hu, Dongdong; Cai, Wenjun; Xu, Zhuangzhi; Bo, Yonghui; Wang, Yushun Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine-Gordon equation with damping. (English) Zbl 07428987 Math. Comput. Simul. 188, 35-59 (2021). MSC: 65-XX 78-XX PDFBibTeX XMLCite \textit{D. Hu} et al., Math. Comput. Simul. 188, 35--59 (2021; Zbl 07428987) Full Text: DOI
Meng, Qing; He, Bin Bifurcation analysis and exact traveling wave solutions for a generic two-dimensional sine-Gordon equation in nonlinear optics. (English) Zbl 1455.34044 J. Appl. Anal. Comput. 10, No. 4, 1443-1463 (2020). MSC: 34C25 34C23 35C07 35L71 78A60 PDFBibTeX XMLCite \textit{Q. Meng} and \textit{B. He}, J. Appl. Anal. Comput. 10, No. 4, 1443--1463 (2020; Zbl 1455.34044) Full Text: DOI
van der Mee, Cornelis Complex short-pulse solutions by gauge transformation. (English) Zbl 1439.35464 J. Geom. Phys. 148, Article ID 103539, 11 p. (2020). MSC: 35Q60 35Q53 78A60 35Q40 82D40 35Q55 45L05 PDFBibTeX XMLCite \textit{C. van der Mee}, J. Geom. Phys. 148, Article ID 103539, 11 p. (2020; Zbl 1439.35464) Full Text: DOI
Monaco, Roberto Traveling electromagnetic waves in annular Josephson tunnel junctions. (English) Zbl 1524.78023 Wave Motion 88, 214-225 (2019). MSC: 78A40 35C07 35L71 PDFBibTeX XMLCite \textit{R. Monaco}, Wave Motion 88, 214--225 (2019; Zbl 1524.78023) Full Text: DOI arXiv
Gul, Zamin; Ali, Amir; Ullah, Arif Localized modes in parametrically driven long Josephson junctions with a double-well potential. (English) Zbl 1422.82031 J. Phys. A, Math. Theor. 52, No. 1, Article ID 015203, 19 p. (2019). MSC: 82D55 35Q55 35B34 35B05 82C80 78A40 PDFBibTeX XMLCite \textit{Z. Gul} et al., J. Phys. A, Math. Theor. 52, No. 1, Article ID 015203, 19 p. (2019; Zbl 1422.82031) Full Text: DOI
Sato, S.; Oguma, K.; Matsuo, T.; Feng, B.-F. A robust numerical integrator for the short pulse equation near criticality. (English) Zbl 1416.78035 J. Comput. Appl. Math. 361, 343-365 (2019). MSC: 78M20 65M06 78A60 PDFBibTeX XMLCite \textit{S. Sato} et al., J. Comput. Appl. Math. 361, 343--365 (2019; Zbl 1416.78035) Full Text: DOI
Ustinov, N. V. Integrable generalizations of the sine-Gordon, short pulse, and reduced Maxwell-Bloch equations. (English) Zbl 1410.35214 J. Math. Phys. 60, No. 1, 013503, 18 p. (2019). MSC: 35Q55 37K15 35C08 78A60 35B44 35Q60 PDFBibTeX XMLCite \textit{N. V. Ustinov}, J. Math. Phys. 60, No. 1, 013503, 18 p. (2019; Zbl 1410.35214) Full Text: DOI
Meng, Gao-Qing; Pan, Yu-Song; Tan, Hao-feng; Xie, Xi-Yang Analytic solutions for the (2+1)-dimensional generalized sine-Gordon equations in nonlinear optics. (English) Zbl 1434.35209 Comput. Math. Appl. 76, No. 6, 1535-1543 (2018). MSC: 35Q60 35L71 78A60 35C08 PDFBibTeX XMLCite \textit{G.-Q. Meng} et al., Comput. Math. Appl. 76, No. 6, 1535--1543 (2018; Zbl 1434.35209) Full Text: DOI
Kiselev, O. M.; Novokshenov, V. Yu. Autoresonance in a model of a terahertz wave generator. (English. Russian original) Zbl 1433.78011 Proc. Steklov Inst. Math. 301, Suppl. 1, S88-S102 (2018); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 23, No. 2, 117-132 (2017). MSC: 78A40 35Q53 78A55 35Q51 35C20 78M35 82D55 PDFBibTeX XMLCite \textit{O. M. Kiselev} and \textit{V. Yu. Novokshenov}, Proc. Steklov Inst. Math. 301, S88--S102 (2018; Zbl 1433.78011); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 23, No. 2, 117--132 (2017) Full Text: DOI
Fu, Yanggeng; Li, Jibin Exact stationary-wave solutions in the standard model of the Kerr-Nonlinear optical fiber with the Bragg grating. (English) Zbl 1474.34282 J. Appl. Anal. Comput. 7, No. 3, 1177-1184 (2017). MSC: 34C37 34C23 34A05 34C25 78A40 35C07 PDFBibTeX XMLCite \textit{Y. Fu} and \textit{J. Li}, J. Appl. Anal. Comput. 7, No. 3, 1177--1184 (2017; Zbl 1474.34282) Full Text: DOI
Macías-Díaz, J. E. Numerical study of the process of nonlinear supratransmission in Riesz space-fractional sine-Gordon equations. (English) Zbl 1485.35400 Commun. Nonlinear Sci. Numer. Simul. 46, 89-102 (2017). MSC: 35R11 35L71 78A25 PDFBibTeX XMLCite \textit{J. E. Macías-Díaz}, Commun. Nonlinear Sci. Numer. Simul. 46, 89--102 (2017; Zbl 1485.35400) Full Text: DOI
Hlaváč, Adam On multisoliton solutions of the constant astigmatism equation. (English) Zbl 1326.35315 J. Phys. A, Math. Theor. 48, No. 36, Article ID 365202, 21 p. (2015). MSC: 35Q53 37K35 78A05 53A05 PDFBibTeX XMLCite \textit{A. Hlaváč}, J. Phys. A, Math. Theor. 48, No. 36, Article ID 365202, 21 p. (2015; Zbl 1326.35315) Full Text: DOI arXiv
Hlaváč, Adam; Marvan, Michal On Lipschitz solutions of the constant astigmatism equation. (English) Zbl 1298.35173 J. Geom. Phys. 85, 88-98 (2014). MSC: 35Q53 35Q74 53A05 78A05 PDFBibTeX XMLCite \textit{A. Hlaváč} and \textit{M. Marvan}, J. Geom. Phys. 85, 88--98 (2014; Zbl 1298.35173) Full Text: DOI
Ivancevic, Vladimir G.; Reid, Darryn J. Controlled complexity in pulse conduction: traveling solitons from neural to optical fibers. (English) Zbl 1366.35178 Math. Eng. Sci. Aerosp. MESA 5, No. 1, 17-32 (2014). Reviewer: Bastian von Harrach (Frankfurt am Main) MSC: 35Q60 78A70 78A60 92C20 35Q92 35Q53 35Q51 PDFBibTeX XMLCite \textit{V. G. Ivancevic} and \textit{D. J. Reid}, Math. Eng. Sci. Aerosp. MESA 5, No. 1, 17--32 (2014; Zbl 1366.35178) Full Text: Link
Debnath, Lokenath Nonlinear partial differential equations for scientists and engineers. 3rd revised ed. (English) Zbl 1242.35001 Basel: Birkhäuser (ISBN 978-0-8176-8264-4/hbk; 978-0-8176-8265-1/ebook). xxiii, 860 p. (2012). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 35-01 35-02 35Q55 35Q53 35Q51 35L65 35L70 81Q05 78A60 47J30 58E30 PDFBibTeX XMLCite \textit{L. Debnath}, Nonlinear partial differential equations for scientists and engineers. 3rd revised ed. Basel: Birkhäuser (2012; Zbl 1242.35001) Full Text: DOI
Yanyushkina, Natalia N.; Belonenko, Mikhail B.; Lebedev, Nikolay G.; Zhukov, Alexander V.; Paliy, Maxim Extremely short optical pulses in carbon nanotubes in dispersive nonmagnetic dielectric media. (English) Zbl 1263.82090 Int. J. Mod. Phys. B 25, No. 25, 3401-3408 (2011). MSC: 82D80 78A25 78A60 82-08 PDFBibTeX XMLCite \textit{N. N. Yanyushkina} et al., Int. J. Mod. Phys. B 25, No. 25, 3401--3408 (2011; Zbl 1263.82090) Full Text: DOI
Pak, A. V.; Yanyushkina, N. N.; Belonenko, M. B.; Lebedev, N. G. Discrete solitons in the bigraphene with adsorbed atomic hydrogen. (English. Russian original) Zbl 1253.82139 Bull. Russ. Acad. Sci., Phys. 75, No. 12, 1655-1657 (2011); translation from Izv. Ross. Akad. Nauk, Ser. Fiz. 75, No. 12, 1760-1762 (2011). MSC: 82D80 78A60 78A50 78A40 35Q51 PDFBibTeX XMLCite \textit{A. V. Pak} et al., Bull. Russ. Acad. Sci., Phys. 75, No. 12, 1655--1657 (2011; Zbl 1253.82139); translation from Izv. Ross. Akad. Nauk, Ser. Fiz. 75, No. 12, 1760--1762 (2011) Full Text: DOI
Ali, Amir; Susanto, Hadi; Wattis, Jonathan A. D. Breathing modes of long Josephson junctions with phase-shifts. (English) Zbl 1222.35123 SIAM J. Appl. Math. 71, No. 1, 242-269 (2011). Reviewer: Jong Hyuk Park (Ulsan) MSC: 35L70 78A40 34D05 34D10 34D20 74K30 PDFBibTeX XMLCite \textit{A. Ali} et al., SIAM J. Appl. Math. 71, No. 1, 242--269 (2011; Zbl 1222.35123) Full Text: DOI arXiv
Shao, Xinping; Han, Danfu On some modified variational iteration methods for solving the one-dimensional sine-Gordon equation. (English) Zbl 1247.37063 Int. J. Comput. Math. 88, No. 5, 969-981 (2011). MSC: 37K10 35Q53 78M30 76M30 65M99 PDFBibTeX XMLCite \textit{X. Shao} and \textit{D. Han}, Int. J. Comput. Math. 88, No. 5, 969--981 (2011; Zbl 1247.37063) Full Text: DOI
Yang, Jianke Nonlinear waves in integrable and nonintegrable systems. (English) Zbl 1234.35006 Mathematical Modeling and Computation 16. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-0-898717-05-1/pbk; 978-0-89871-968-0/ebook). xxvi, 430 p. (2010). Reviewer: Georg Hebermehl (Berlin) MSC: 35-02 37-02 65-02 35Q55 35Q41 35Q51 35J10 35P10 37K10 37K15 65N25 65N35 37K40 78A60 82C10 PDFBibTeX XMLCite \textit{J. Yang}, Nonlinear waves in integrable and nonintegrable systems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2010; Zbl 1234.35006) Full Text: DOI
Bao, Weizhu; Dong, Xuanchun; Xin, Jack Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse. (English) Zbl 1190.35205 Physica D 239, No. 13, 1120-1134 (2010). MSC: 35Q55 78A60 35B40 65M22 PDFBibTeX XMLCite \textit{W. Bao} et al., Physica D 239, No. 13, 1120--1134 (2010; Zbl 1190.35205) Full Text: DOI
Dauxois, Thierry; Peyrard, Michel Physics of solitons. Reprint of the 2006 original. (English) Zbl 1204.35141 Cambridge: Cambridge University Press (ISBN 978-0-521-14360-8/pbk; 978-0-521-85421-4/hbk). xii, 422 p. (2010). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q51 35-02 35Q53 35Q55 37K40 76B15 78A60 81V80 PDFBibTeX XMLCite \textit{T. Dauxois} and \textit{M. Peyrard}, Physics of solitons. Reprint of the 2006 original. Cambridge: Cambridge University Press (2010; Zbl 1204.35141)
Molotkov, I. A. Fine structure of the soliton signal in the magnetic chain in an external magnetic field near a critical value. (English) Zbl 1179.78010 Russ. J. Math. Phys. 16, No. 2, 290-295 (2009). MSC: 78A05 35Q51 78A40 37K40 PDFBibTeX XMLCite \textit{I. A. Molotkov}, Russ. J. Math. Phys. 16, No. 2, 290--295 (2009; Zbl 1179.78010) Full Text: DOI
Bratsos, A. G. An improved numerical scheme for the sine-Gordon equation in 2+1 dimensions. (English) Zbl 1195.78075 Int. J. Numer. Methods Eng. 75, No. 7, 787-799 (2008). MSC: 78M20 78A55 82D55 PDFBibTeX XMLCite \textit{A. G. Bratsos}, Int. J. Numer. Methods Eng. 75, No. 7, 787--799 (2008; Zbl 1195.78075) Full Text: DOI
Belonenko, M. B.; Glazov, S. Yu.; Meshcheryakova, N. E. Interaction of wide-spectrum electromagnetic pulses with materials containing a superstructure. (English. Russian original) Zbl 1179.78091 Bull. Russ. Acad. Sci., Phys. 72, No. 12, 1610-1613 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Fiz. 72, No. 12, 1704-1707 (2008). MSC: 78A60 35L70 81V80 PDFBibTeX XMLCite \textit{M. B. Belonenko} et al., Bull. Russ. Acad. Sci., Phys. 72, No. 12, 1610--1613 (2008; Zbl 1179.78091); translation from Izv. Ross. Akad. Nauk, Ser. Fiz. 72, No. 12, 1704--1707 (2008) Full Text: DOI
Andreev, V. A. System of equations for stimulated combination scattering and the related double periodic \(A _n^{(1)}\) Toda chains. (English. Russian original) Zbl 1185.37152 Theor. Math. Phys. 156, No. 1, 1020-1027 (2008); translation from Teor. Mat. Fiz. 156, No. 1, 67-76 (2008). Reviewer: Michal Marvan (Opava) MSC: 37K15 37K35 78A45 PDFBibTeX XMLCite \textit{V. A. Andreev}, Theor. Math. Phys. 156, No. 1, 1020--1027 (2008; Zbl 1185.37152); translation from Teor. Mat. Fiz. 156, No. 1, 67--76 (2008) Full Text: DOI
Matsuno, Yoshimasa Periodic solutions of the short pulse model equation. (English) Zbl 1152.81554 J. Math. Phys. 49, No. 7, 073508, 18 p. (2008). MSC: 35Q53 35B10 35L70 78A60 PDFBibTeX XMLCite \textit{Y. Matsuno}, J. Math. Phys. 49, No. 7, 073508, 18 p. (2008; Zbl 1152.81554) Full Text: DOI
Susanto, H.; Van Gils, S. A. Existence and stability analysis of solitary waves in a tricrystal junction. (English) Zbl 1136.35450 Phys. Lett., A 338, No. 3-5, 239-246 (2005). MSC: 35Q53 78A60 PDFBibTeX XMLCite \textit{H. Susanto} and \textit{S. A. Van Gils}, Phys. Lett., A 338, No. 3--5, 239--246 (2005; Zbl 1136.35450) Full Text: DOI
Katriel, Guy Existence of travelling waves in discrete sine-Gordon rings. (English) Zbl 1086.34027 SIAM J. Math. Anal. 36, No. 5, 1434-1443 (2005). MSC: 34B45 34C60 78A55 34B15 PDFBibTeX XMLCite \textit{G. Katriel}, SIAM J. Math. Anal. 36, No. 5, 1434--1443 (2005; Zbl 1086.34027) Full Text: DOI arXiv
Sakovich, Anton; Sakovich, Sergei The short pulse equation is integrals. (English) Zbl 1067.35115 J. Phys. Soc. Japan 74, No. 1, 239-241 (2005). MSC: 35Q55 37K10 78A60 PDFBibTeX XMLCite \textit{A. Sakovich} and \textit{S. Sakovich}, J. Phys. Soc. Japan 74, No. 1, 239--241 (2005; Zbl 1067.35115) Full Text: DOI arXiv
Minzoni, A. A.; Smyth, Noel F.; Worthy, Annette L. Evolution of two-dimensional standing and travelling breather solutions for the sine-Gordon equation. (English) Zbl 1051.35074 Physica D 189, No. 3-4, 167-187 (2004). MSC: 35Q53 37K40 35L70 78A60 PDFBibTeX XMLCite \textit{A. A. Minzoni} et al., Physica D 189, No. 3--4, 167--187 (2004; Zbl 1051.35074) Full Text: DOI
Moloney, Jerome; Newell, Alan Nonlinear optics. (English) Zbl 1054.78001 Boulder, CO: Westview Press (ISBN 0-8133-4118-3/pbk). x, 440 p. (2004). Reviewer: Georg Hebermehl (Berlin) MSC: 78-01 78A60 PDFBibTeX XMLCite \textit{J. Moloney} and \textit{A. Newell}, Nonlinear optics. Boulder, CO: Westview Press (2004; Zbl 1054.78001)
Tian, Qiang; Wang, Jingping Solitons and breathers of electromagnetic wave in superlattices. (English) Zbl 1016.78003 Int. J. Theor. Phys. 41, No. 7, 1275-1279 (2002). MSC: 78A40 35Q51 35Q60 35Q53 81V80 PDFBibTeX XMLCite \textit{Q. Tian} and \textit{J. Wang}, Int. J. Theor. Phys. 41, No. 7, 1275--1279 (2002; Zbl 1016.78003) Full Text: DOI
Benabdallah, A.; Caputo, J. G.; Flytzanis, N. The window Josephson junction: a coupled linear nonlinear system. (English) Zbl 1052.78001 Physica D 161, No. 1-2, 79-101 (2002). MSC: 78A25 35Q53 35Q51 PDFBibTeX XMLCite \textit{A. Benabdallah} et al., Physica D 161, No. 1--2, 79--101 (2002; Zbl 1052.78001) Full Text: DOI arXiv
Kapitula, Todd; Kevrekidis, Panayotis Stability of waves in discrete systems. (English) Zbl 1001.37080 Nonlinearity 14, No. 3, 533-566 (2001). Reviewer: Jan Cholewa (Katowice) MSC: 37K45 37K10 35R10 39A12 78A60 PDFBibTeX XMLCite \textit{T. Kapitula} and \textit{P. Kevrekidis}, Nonlinearity 14, No. 3, 533--566 (2001; Zbl 1001.37080) Full Text: DOI
Xin, J. X. Modeling light bullets with the two-dimensional sine-Gordon equation. (English) Zbl 0936.78006 Physica D 135, No. 3-4, 345-368 (2000). MSC: 78A60 35Q60 35Q53 PDFBibTeX XMLCite \textit{J. X. Xin}, Physica D 135, No. 3--4, 345--368 (2000; Zbl 0936.78006) Full Text: DOI
Belokolos, E. D.; Enolskii, V. Z.; Korostil, A. M. Two-phase nonlinear waves in the long Josephson junction. (English) Zbl 0935.78012 Physica D 116, No. 1-2, 253-269 (1998). MSC: 78A99 35Q60 82D55 37K20 PDFBibTeX XMLCite \textit{E. D. Belokolos} et al., Physica D 116, No. 1--2, 253--269 (1998; Zbl 0935.78012) Full Text: DOI
Stuart, David M. Solitons on pseudo-Riemannian manifolds. I: The sine-Gordon equation. (English) Zbl 0935.35143 Commun. Partial Differ. Equations 23, No. 9-10, 1815-1837 (1998). Reviewer: P.Laubin (Liège) MSC: 35Q53 37K40 78A05 PDFBibTeX XMLCite \textit{D. M. Stuart}, Commun. Partial Differ. Equations 23, No. 9--10, 1815--1837 (1998; Zbl 0935.35143) Full Text: DOI
Maksimov, A. G.; Nekorkin, V. I.; Rabinovich, M. I. Soliton trains and I-V characteristics of long Josephson junctions. (English) Zbl 0889.35092 Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 2, 491-505 (1995). MSC: 35Q53 78A35 82D55 PDFBibTeX XMLCite \textit{A. G. Maksimov} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 2, 491--505 (1995; Zbl 0889.35092) Full Text: DOI
McLaughlin, David W.; Muraki, David J.; Shelley, Michael J. Light interacting with liquid crystals. (English) Zbl 0790.35099 Physica D 68, No. 1, 116-126 (1993). MSC: 35Q53 82D30 78A60 PDFBibTeX XMLCite \textit{D. W. McLaughlin} et al., Physica D 68, No. 1, 116--126 (1993; Zbl 0790.35099) Full Text: DOI
Bountis, Tassos; Skiniotis, Takis Inductively coupled long Josephson junctions: Collective coordinate analysis and I-V characteristics. (English) Zbl 0900.35397 Christiansen, P. L. (ed.) et al., Future directions of nonlinear dynamics in physical and biological systems. Proceedings of a NATO Advanced Study Institute in honour of Alwyn Scott’s 60th birthday, Lyngby, Denmark, July 23–August 1, 1992. New York, NY: Plenum. NATO ASI Ser., Ser. B, Phys. 312, 267-281 (1993). MSC: 35Q60 82D55 78A55 PDFBibTeX XMLCite \textit{T. Bountis} and \textit{T. Skiniotis}, NATO ASI Ser., Ser. B, Phys. 312, 267--281 (1993; Zbl 0900.35397)
Meinel, Reinhard; Neugebauer, Gernot; Steudel, Heinz Solitons. Nonlinear structures. (Solitonen. Nichtlineare Strukturen.) (German) Zbl 0743.35062 Berlin: Akademie-Verlag. 192 S. (1991). Reviewer: G.Oevel (Loughborough) MSC: 35Q51 35P25 35-01 58J72 78A60 76X05 PDFBibTeX XMLCite \textit{R. Meinel} et al., Solitonen. Nichtlineare Strukturen. Berlin: Akademie-Verlag (1991; Zbl 0743.35062)
Christiansen, Peter Leth Soliton dynamic states in the sine-Gordon system. (English) Zbl 0546.65086 Wave phenomena: modern theory and applications, int. Meet. Univ. Toronto 1983, North-Holland Math. Stud. 97, 349-360 (1984). MSC: 65Z05 65N22 78A40 81Q05 35Q99 PDFBibTeX XML
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Miranker, W. L.; Bandes, K. A functional relation and an acceleration procedure for calculating the voltage response of Josephson junctions. (English) Zbl 0441.65093 J. Comput. Phys. 37, 274-279 (1980). MSC: 65Z05 78A25 35Q99 65B05 65N12 PDFBibTeX XMLCite \textit{W. L. Miranker} and \textit{K. Bandes}, J. Comput. Phys. 37, 274--279 (1980; Zbl 0441.65093) Full Text: DOI