Biondini, Gino; Luo, Xu-Dan; Oregero, Jeffrey; Tovbis, Alexander Elliptic finite-band potentials of a non-self-adjoint Dirac operator. (English) Zbl 07716356 Adv. Math. 429, Article ID 109188, 63 p. (2023). MSC: 35Q55 35Q53 35Q51 35C08 37K15 37K35 47A10 PDFBibTeX XMLCite \textit{G. Biondini} et al., Adv. Math. 429, Article ID 109188, 63 p. (2023; Zbl 07716356) Full Text: DOI arXiv
Abeya, Asela; Biondini, Gino; Hoefer, Mark A. Whitham modulation theory for the defocusing nonlinear Schrödinger equation in two and three spatial dimensions. (English) Zbl 1517.35198 J. Phys. A, Math. Theor. 56, No. 2, Article ID 025701, 34 p. (2023). MSC: 35Q55 35C07 35C08 35C09 PDFBibTeX XMLCite \textit{A. Abeya} et al., J. Phys. A, Math. Theor. 56, No. 2, Article ID 025701, 34 p. (2023; Zbl 1517.35198) Full Text: DOI arXiv
Abeya, Asela; Biondini, Gino; Prinari, Barbara Manakov system with parity symmetry on nonzero background and associated boundary value problems. (English) Zbl 1507.35246 J. Phys. A, Math. Theor. 55, No. 25, Article ID 254001, 40 p. (2022). MSC: 35Q55 35C08 PDFBibTeX XMLCite \textit{A. Abeya} et al., J. Phys. A, Math. Theor. 55, No. 25, Article ID 254001, 40 p. (2022; Zbl 1507.35246) Full Text: DOI
Biondini, Gino; Lottes, Jonathan; Mantzavinos, Dionyssios Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows. (English) Zbl 1472.35347 Stud. Appl. Math. 146, No. 2, 371-439 (2021). MSC: 35Q55 35Q15 35C08 35B40 35P25 37K15 37K10 35R30 PDFBibTeX XMLCite \textit{G. Biondini} et al., Stud. Appl. Math. 146, No. 2, 371--439 (2021; Zbl 1472.35347) Full Text: DOI arXiv
Biondini, Gino; Li, Sitai; Mantzavinos, Dionyssios Long-time asymptotics for the focusing nonlinear Schrödinger equation with nonzero boundary conditions in the presence of a discrete spectrum. (English) Zbl 1464.35309 Commun. Math. Phys. 382, No. 3, 1495-1577 (2021). MSC: 35Q55 35A22 35P25 35G10 35K25 35B40 35C08 35B34 37K15 PDFBibTeX XMLCite \textit{G. Biondini} et al., Commun. Math. Phys. 382, No. 3, 1495--1577 (2021; Zbl 1464.35309) Full Text: DOI arXiv
Koutsokostas, Georgios N.; Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.; Prinari, Barbara; Biondini, Gino Multiscale expansions avector solitons of a two-dimensional nonlocal nonlinear Schrödinger system. (English) Zbl 1454.78038 Stud. Appl. Math. 145, No. 4, 739-764 (2020). MSC: 78A60 35Q55 78M34 35Q53 35C08 37K10 PDFBibTeX XMLCite \textit{G. N. Koutsokostas} et al., Stud. Appl. Math. 145, No. 4, 739--764 (2020; Zbl 1454.78038) Full Text: DOI
Biondini, Gino; Oregero, Jeffrey Semiclassical dynamics and coherent soliton condensates in self-focusing nonlinear media with periodic initial conditions. (English) Zbl 1454.35332 Stud. Appl. Math. 145, No. 3, 325-356 (2020). MSC: 35Q55 81Q20 35P25 35C08 35B40 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{J. Oregero}, Stud. Appl. Math. 145, No. 3, 325--356 (2020; Zbl 1454.35332) Full Text: DOI arXiv
Plaisier Leisman, Katelyn; Biondini, Gino; Kovacic, Gregor Linearizable boundary value problems for the nonlinear Schrödinger equation in laboratory coordinates. (English) Zbl 1471.35260 Phys. Lett., A 383, No. 6, 494-503 (2019). MSC: 35Q55 34L40 PDFBibTeX XMLCite \textit{K. Plaisier Leisman} et al., Phys. Lett., A 383, No. 6, 494--503 (2019; Zbl 1471.35260) Full Text: DOI arXiv
Biondini, Gino; Wang, Qiao Discrete and continuous coupled nonlinear integrable systems via the dressing method. (English) Zbl 1420.35342 Stud. Appl. Math. 142, No. 2, 139-161 (2019). MSC: 35Q55 35Q15 37K10 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{Q. Wang}, Stud. Appl. Math. 142, No. 2, 139--161 (2019; Zbl 1420.35342) Full Text: DOI arXiv
Biondini, Gino; Luo, Xudan Imaginary eigenvalues of Zakharov-Shabat problems with non-zero background. (English) Zbl 1404.35402 Phys. Lett., A 382, No. 37, 2632-2637 (2018). MSC: 35Q55 47J10 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{X. Luo}, Phys. Lett., A 382, No. 37, 2632--2637 (2018; Zbl 1404.35402) Full Text: DOI
Biondini, Gino; Li, Sitai; Mantzavinos, Dionyssios; Trillo, Stefano Universal behavior of modulationally unstable media. (English) Zbl 1403.35271 SIAM Rev. 60, No. 4, 888-908 (2018). MSC: 35Q55 37K40 74J30 35R09 35B20 PDFBibTeX XMLCite \textit{G. Biondini} et al., SIAM Rev. 60, No. 4, 888--908 (2018; Zbl 1403.35271) Full Text: DOI arXiv
Pichler, Monika; Biondini, Gino On the focusing non-linear Schrödinger equation with non-zero boundary conditions and double poles. (English) Zbl 1406.35368 IMA J. Appl. Math. 82, No. 1, 131-151 (2017). MSC: 35Q55 35C08 35B40 37K15 35P25 35R30 45Q05 PDFBibTeX XMLCite \textit{M. Pichler} and \textit{G. Biondini}, IMA J. Appl. Math. 82, No. 1, 131--151 (2017; Zbl 1406.35368) Full Text: DOI
Biondini, Gino; Mantzavinos, Dionyssios Long-time asymptotics for the focusing nonlinear Schrödinger equation with nonzero boundary conditions at infinity and asymptotic stage of modulational instability. (English) Zbl 1379.35286 Commun. Pure Appl. Math. 70, No. 12, 2300-2365 (2017). MSC: 35Q55 35B40 37K15 35Q15 33E05 35R30 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{D. Mantzavinos}, Commun. Pure Appl. Math. 70, No. 12, 2300--2365 (2017; Zbl 1379.35286) Full Text: DOI arXiv
Li, Sitai; Biondini, Gino; Schiebold, Cornelia On the degenerate soliton solutions of the focusing nonlinear Schrödinger equation. (English) Zbl 1365.35159 J. Math. Phys. 58, No. 3, 033507, 27 p. (2017). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q55 35C07 35C08 35P25 37K15 37K40 PDFBibTeX XMLCite \textit{S. Li} et al., J. Math. Phys. 58, No. 3, 033507, 27 p. (2017; Zbl 1365.35159) Full Text: DOI Link
Biondini, Gino; Fagerstrom, Emily; Prinari, Barbara Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions. (English) Zbl 1415.35217 Physica D 333, 117-136 (2016). MSC: 35P25 35Q55 37K10 PDFBibTeX XMLCite \textit{G. Biondini} et al., Physica D 333, 117--136 (2016; Zbl 1415.35217) Full Text: DOI
Biondini, Gino; Mantzavinos, Dionyssios Universal nature of the nonlinear stage of modulational instability. (English) Zbl 1356.35214 Phys. Rev. Lett. 116, No. 4, Article ID 043902, 5 p. (2016). MSC: 35Q55 35B40 35B30 35B35 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{D. Mantzavinos}, Phys. Rev. Lett. 116, No. 4, Article ID 043902, 5 p. (2016; Zbl 1356.35214) Full Text: DOI arXiv
Biondini, Gino; Kraus, Daniel K.; Prinari, Barbara The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions. (English) Zbl 1365.35148 Commun. Math. Phys. 348, No. 2, 475-533 (2016). Reviewer: Thomas J. Bartsch (Gießen) MSC: 35Q55 37K15 35C08 35P25 PDFBibTeX XMLCite \textit{G. Biondini} et al., Commun. Math. Phys. 348, No. 2, 475--533 (2016; Zbl 1365.35148) Full Text: DOI arXiv
Biondini, Gino (ed.); Fokas, Athanassios S. (ed.) Preface: Mark J. Ablowitz, Nonlinear waves and integrable systems. I. (English) Zbl 1347.35005 Stud. Appl. Math. 137, No. 1, 3-9 (2016). MSC: 35-03 37-03 78-03 01A60 01A61 35Q55 35Q53 37K10 37K15 78A60 01A70 PDFBibTeX XMLCite \textit{G. Biondini} (ed.) and \textit{A. S. Fokas} (ed.), Stud. Appl. Math. 137, No. 1, 3--9 (2016; Zbl 1347.35005) Full Text: DOI
Biondini, G.; Fokas, A. S.; Shepelsky, D. Evolution problems: nonlinear. (English) Zbl 1346.65045 Fokas, Athanassios S. (ed.) et al., Unified transform for boundary value problems. Applications and advances. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-61197-381-5/pbk; 978-1-61197-382-2/ebook). Other Titles in Applied Mathematics 141, 49-60 (2015). MSC: 65M22 35Q55 PDFBibTeX XMLCite \textit{G. Biondini} et al., Other Titles Appl. Math. 141, 49--60 (2015; Zbl 1346.65045)
Kraus, Daniel; Biondini, Gino; Kovačič, Gregor The focusing Manakov system with nonzero boundary conditions. (English) Zbl 1330.35406 Nonlinearity 28, No. 9, 3101-3151 (2015). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q55 37K15 34L25 35C08 35P10 PDFBibTeX XMLCite \textit{D. Kraus} et al., Nonlinearity 28, No. 9, 3101--3151 (2015; Zbl 1330.35406) Full Text: DOI Link
Biondini, Gino; Kraus, Daniel K.; Prinari, Barbara; Vitale, Federica Polarization interactions in multi-component defocusing media. (English) Zbl 1331.35314 J. Phys. A, Math. Theor. 48, No. 39, Article ID 395202, 13 p. (2015). Reviewer: Qin Meng Zhao (Beijing) MSC: 35Q55 37K15 35C08 35R30 78A60 PDFBibTeX XMLCite \textit{G. Biondini} et al., J. Phys. A, Math. Theor. 48, No. 39, Article ID 395202, 13 p. (2015; Zbl 1331.35314) Full Text: DOI
Biondini, Gino; Bui, Anh The Ablowitz-Ladik system with linearizable boundary conditions. (English) Zbl 1333.35246 J. Phys. A, Math. Theor. 48, No. 37, Article ID 375202, 31 p. (2015). Reviewer: Xingbin Pan (Shanghai) MSC: 35Q55 35C08 35Q51 37K35 81U40 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{A. Bui}, J. Phys. A, Math. Theor. 48, No. 37, Article ID 375202, 31 p. (2015; Zbl 1333.35246) Full Text: DOI
Prinari, Barbara; Vitale, Federica; Biondini, Gino Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions. (English) Zbl 1321.35212 J. Math. Phys. 56, No. 7, 071505, 33 p. (2015). MSC: 35Q55 35C08 35J66 37K10 78A60 78A46 82B10 PDFBibTeX XMLCite \textit{B. Prinari} et al., J. Math. Phys. 56, No. 7, 071505, 33 p. (2015; Zbl 1321.35212) Full Text: DOI Link
Biondini, Gino; Fagerstrom, Emily The integrable nature of modulational instability. (English) Zbl 1330.35395 SIAM J. Appl. Math. 75, No. 1, 136-163 (2015). Reviewer: Natalia Bondarenko (Saratov) MSC: 35Q55 37K15 37K40 37K45 34L25 34L40 74J25 74J30 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{E. Fagerstrom}, SIAM J. Appl. Math. 75, No. 1, 136--163 (2015; Zbl 1330.35395) Full Text: DOI Link
Biondini, Gino; Kraus, Daniel Inverse scattering transform for the defocusing Manakov system with nonzero boundary conditions. (English) Zbl 1339.35282 SIAM J. Math. Anal. 47, No. 1, 706-757 (2015). Reviewer: Yvan Martel (Palaiseau) MSC: 35Q55 35Q15 35Q51 37K15 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{D. Kraus}, SIAM J. Math. Anal. 47, No. 1, 706--757 (2015; Zbl 1339.35282) Full Text: DOI Link
Biondini, Gino; Prinari, Barbara On the spectrum of the Dirac operator and the existence of discrete eigenvalues for the defocusing nonlinear Schrödinger equation. (English) Zbl 1291.35335 Stud. Appl. Math. 132, No. 2, 138-159 (2014). MSC: 35Q55 35Q51 35P25 35C08 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{B. Prinari}, Stud. Appl. Math. 132, No. 2, 138--159 (2014; Zbl 1291.35335) Full Text: DOI
Biondini, Gino; Kovačič, Gregor Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions. (English) Zbl 1298.35187 J. Math. Phys. 55, No. 3, 031506, 22 p. (2014). Reviewer: Chengbo Wang (Hangzhou) MSC: 35Q55 35Q15 35P25 35B40 35R30 35C08 37K15 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{G. Kovačič}, J. Math. Phys. 55, No. 3, 031506, 22 p. (2014; Zbl 1298.35187) Full Text: DOI Link
Biondini, Gino; Bui, A. On the nonlinear Schrödinger equation on the half line with homogeneous Robin boundary conditions. (English) Zbl 1277.35312 Stud. Appl. Math. 129, No. 3, 249-271 (2012). MSC: 35Q55 37K35 35C08 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{A. Bui}, Stud. Appl. Math. 129, No. 3, 249--271 (2012; Zbl 1277.35312) Full Text: DOI
Prinari, Barbara; Biondini, Gino; Trubatch, A. David Inverse scattering transform for the multi-component nonlinear Schrödinger equation with nonzero boundary conditions. (English) Zbl 1218.35251 Stud. Appl. Math. 126, No. 3, 245-302 (2011). Reviewer: Michael Perelmuter (Kyïv) MSC: 35R30 35Q55 35P25 81U40 PDFBibTeX XMLCite \textit{B. Prinari} et al., Stud. Appl. Math. 126, No. 3, 245--302 (2011; Zbl 1218.35251) Full Text: DOI
Biondini, Gino; Hwang, Guenbo Solitons, boundary value problems and a nonlinear method of images. (English) Zbl 1173.35675 J. Phys. A, Math. Theor. 42, No. 20, Article ID 205207, 18 p. (2009). MSC: 35Q55 35Q51 35P25 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{G. Hwang}, J. Phys. A, Math. Theor. 42, No. 20, Article ID 205207, 18 p. (2009; Zbl 1173.35675) Full Text: DOI arXiv
Biondini, Gino; Hwang, Guenbo Initial-boundary-value problems for discrete evolution equations: discrete linear Schrödinger and integrable discrete nonlinear Schrödinger equations. (English) Zbl 1157.35115 Inverse Probl. 24, No. 6, Article ID 065011, 44 p. (2008). MSC: 35R10 35Q55 39A12 35A35 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{G. Hwang}, Inverse Probl. 24, No. 6, Article ID 065011, 44 p. (2008; Zbl 1157.35115) Full Text: DOI arXiv
Moore, R. O.; Biondini, G.; Kath, W. L. A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons. (English) Zbl 1153.35073 SIAM Rev. 50, No. 3, 523-549 (2008). MSC: 35Q55 35Q51 65C20 65C05 78A40 PDFBibTeX XMLCite \textit{R. O. Moore} et al., SIAM Rev. 50, No. 3, 523--549 (2008; Zbl 1153.35073) Full Text: DOI
Moore, R. O.; Biondini, G.; Kath, W. L. A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons. (English) Zbl 1128.35097 SIAM J. Appl. Math. 67, No. 5, 1418-1439 (2007). MSC: 35Q55 65C05 78A60 94A20 65C20 PDFBibTeX XMLCite \textit{R. O. Moore} et al., SIAM J. Appl. Math. 67, No. 5, 1418--1439 (2007; Zbl 1128.35097) Full Text: DOI
Ablowitz, Mark J.; Biondini, Gino; Prinari, Barbara Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions. (English) Zbl 1127.35059 Inverse Probl. 23, No. 4, 1711-1758 (2007). MSC: 35Q55 37K15 35Q15 35R30 PDFBibTeX XMLCite \textit{M. J. Ablowitz} et al., Inverse Probl. 23, No. 4, 1711--1758 (2007; Zbl 1127.35059) Full Text: DOI Link
Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions. (English) Zbl 1112.37070 J. Math. Phys. 47, No. 6, 063508, 33 p. (2006). MSC: 37K15 34A55 34L25 35P25 35Q55 35R30 81U40 PDFBibTeX XMLCite \textit{B. Prinari} et al., J. Math. Phys. 47, No. 6, 063508, 33 p. (2006; Zbl 1112.37070) Full Text: DOI
Biondini, G.; Kodama, Y. On the Whitham equations for the defocusing nonlinear Schrödinger equation with step initial data. (English) Zbl 1110.35080 J. Nonlinear Sci. 16, No. 5, 435-481 (2006). MSC: 35Q55 78A60 37K10 37K40 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{Y. Kodama}, J. Nonlinear Sci. 16, No. 5, 435--481 (2006; Zbl 1110.35080) Full Text: DOI arXiv
Ablowitz, M. J.; Ahrens, C.; Biondini, G.; Chakravarty, S.; Docherty, A. Periodic-group-delay dispersion compensation reduces collision-induced timing shifts in dispersion-managed quasilinear systems. (English) Zbl 1178.35341 Theor. Math. Phys. 144, No. 1, 881-887 (2005); translation from Teor. Mat. Fiz. 144, No. 1, 6-13 (2005). MSC: 35Q55 78A60 35A30 PDFBibTeX XMLCite \textit{M. J. Ablowitz} et al., Theor. Math. Phys. 144, No. 1, 881--887 (2005; Zbl 1178.35341); translation from Teor. Mat. Fiz. 144, No. 1, 6--13 (2005) Full Text: DOI
Chakravarty, Sarbarish; Biondini, Gino On the characteristic parameters of dispersion-managed optical pulses. (English) Zbl 1053.35540 Ablowitz, M. J. (ed.) et al., Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 – July 6, 2002. River Edge, NJ: World Scientific (ISBN 981-238-270-4). 351-358 (2003). MSC: 35Q55 78A60 PDFBibTeX XMLCite \textit{S. Chakravarty} and \textit{G. Biondini}, in: Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 -- July 6, 2002. River Edge, NJ: World Scientific. 351--358 (2003; Zbl 1053.35540)
Moore, R. O.; Biondini, G.; Kath, W. L. Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems. (English) Zbl 1053.78506 Ablowitz, M. J. (ed.) et al., Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 – July 6, 2002. River Edge, NJ: World Scientific (ISBN 981-238-270-4). 383-390 (2003). MSC: 78A60 35Q55 65C05 PDFBibTeX XMLCite \textit{R. O. Moore} et al., in: Nonlinear physics: theory and experiment II. Proceedings of the workshop, Gallipoli, Italy, June 27 -- July 6, 2002. River Edge, NJ: World Scientific. 383--390 (2003; Zbl 1053.78506)
Ablowitz, M. J.; Biondini, G.; Chakravarty, S. Soliton communications and wavelength-division multiplexing. (English) Zbl 0940.35182 DeSanto, John A. (ed.), Mathematical and numerical aspects of wave propagation. Proceedings of the 4th international conference held at Mines in Golden, CO, USA, June 1-5, 1998. Philadelphia, PA: SIAM. Proc. Appl. Math. 145-149 (1998). MSC: 35Q55 78A60 94A05 PDFBibTeX XMLCite \textit{M. J. Ablowitz} et al., Proc. Appl. Math. 145--149, 145--149 (1998; Zbl 0940.35182)
Ablowitz, M. J.; Biondini, G.; De Lillo, S. On the well-posedness of the Eckhaus equation. (English) Zbl 1052.35513 Phys. Lett., A 230, No. 5-6, 319-323 (1997). MSC: 35Q55 PDFBibTeX XMLCite \textit{M. J. Ablowitz} et al., Phys. Lett., A 230, No. 5--6, 319--323 (1997; Zbl 1052.35513) Full Text: DOI
Biondini, G.; De Lillo, S. Stochastic effects of NLS solitons. (English) Zbl 0916.35144 Vázquez, Luis (ed.) et al., Proceedings of the Euroconference on nonlinear Klein-Gordon and Schrödinger systems: theory and applications, Madrid, Spain, September 25–30, 1995. Singapore: World Scientific. 262-265 (1996). MSC: 35R60 35Q55 PDFBibTeX XMLCite \textit{G. Biondini} and \textit{S. De Lillo}, in: Proceedings of the Euroconference on nonlinear Klein-Gordon and Schrödinger systems: theory and applications, Madrid, Spain, September 25--30, 1995. Singapore: World Scientific. 262--265 (1996; Zbl 0916.35144)
Biondini, G.; De Lillo, S.; Calogero, F. The \((2+1)\)-dimensional Eckhaus equation: Display of some solutions. (English) Zbl 0982.35104 Makhanov, V. G. (ed.) et al., Nonlinear evolution equations and dynamical systems. NEEDS ’94. Proceedings of the 10th international workshop, Los Alamos, NM, USA, September 11-18, 1994. Singapore: World Scientific. 16-23 (1995). MSC: 35Q55 37K40 PDFBibTeX XMLCite \textit{G. Biondini} et al., in: Nonlinear evolution equations and dynamical systems. NEEDS '94. Proceedings of the 10th international workshop, Los Alamos, NM, USA, September 11--18, 1994. Singapore: World Scientific. 16--23 (1995; Zbl 0982.35104)