Klein, Christian; Prada-Malagon, Juan; Stoilov, Nikola On numerical approaches to nonlinear Schrödinger and Korteweg-de Vries equations for piecewise smooth and slowly decaying initial data. (English) Zbl 07736401 Physica D 454, Article ID 133885, 12 p. (2023). MSC: 65-XX 37-XX PDFBibTeX XMLCite \textit{C. Klein} et al., Physica D 454, Article ID 133885, 12 p. (2023; Zbl 07736401) Full Text: DOI
Carles, Rémi; Klein, Christian; Sparber, Christof On ground state (in-)stability in multi-dimensional cubic-quintic Schrödinger equations. (English) Zbl 1515.35242 ESAIM, Math. Model. Numer. Anal. 57, No. 2, 423-443 (2023). MSC: 35Q55 35Q41 35C08 35B35 35B10 65M70 49M41 PDFBibTeX XMLCite \textit{R. Carles} et al., ESAIM, Math. Model. Numer. Anal. 57, No. 2, 423--443 (2023; Zbl 1515.35242) Full Text: DOI
Frauendiener, Jörg; Klein, Christian; Muhammad, Umar; Stoilov, Nikola Numerical study of Davey-Stewartson I systems. (English) Zbl 07779107 Stud. Appl. Math. 149, No. 1, 76-94 (2022). MSC: 65M70 65L06 35B44 37K10 35C08 35C06 35Q55 35Q41 PDFBibTeX XMLCite \textit{J. Frauendiener} et al., Stud. Appl. Math. 149, No. 1, 76--94 (2022; Zbl 07779107) Full Text: DOI arXiv OA License
Duchêne, Vincent; Klein, Christian Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart. (English) Zbl 1503.65259 Discrete Contin. Dyn. Syst., Ser. B 27, No. 10, 5905-5933 (2022). Reviewer: Anouar Ben Mabrouk (Monastir) MSC: 65M70 65F10 65L06 35Q35 76B15 35B35 35C08 35B05 35B44 PDFBibTeX XMLCite \textit{V. Duchêne} and \textit{C. Klein}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 10, 5905--5933 (2022; Zbl 1503.65259) Full Text: DOI arXiv
Klein, Christian; Stoilov, Nikola Spectral approach to Korteweg-de Vries equations on the compactified real line. (English) Zbl 1484.65259 Appl. Numer. Math. 177, 160-170 (2022). MSC: 65M70 PDFBibTeX XMLCite \textit{C. Klein} and \textit{N. Stoilov}, Appl. Numer. Math. 177, 160--170 (2022; Zbl 1484.65259) Full Text: DOI arXiv
Arnold, Anton; Klein, Christian; Ujvari, Bernhard WKB-method for the 1D Schrödinger equation in the semi-classical limit: enhanced phase treatment. (English) Zbl 1495.65126 BIT 62, No. 1, 1-22 (2022). MSC: 65L60 34L40 34E20 81Q20 PDFBibTeX XMLCite \textit{A. Arnold} et al., BIT 62, No. 1, 1--22 (2022; Zbl 1495.65126) Full Text: DOI arXiv
Klein, Christian; Stoilov, Nikola Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations. (English) Zbl 07508515 J. Comput. Phys. 434, Article ID 110149, 16 p. (2021). MSC: 65Mxx 83Cxx 35Qxx PDFBibTeX XMLCite \textit{C. Klein} and \textit{N. Stoilov}, J. Comput. Phys. 434, Article ID 110149, 16 p. (2021; Zbl 07508515) Full Text: DOI arXiv
Klein, Christian; Riton, Julien; Stoilov, Nikola Multi-domain spectral approach for the Hilbert transform on the real line. (English) Zbl 1490.44005 SN Partial Differ. Equ. Appl. 2, No. 3, Paper No. 36, 19 p. (2021). MSC: 44A15 42B20 65R10 PDFBibTeX XMLCite \textit{C. Klein} et al., SN Partial Differ. Equ. Appl. 2, No. 3, Paper No. 36, 19 p. (2021; Zbl 1490.44005) Full Text: DOI arXiv
Klein, Christian; Stoilov, Nikola Numerical study of break-up in solutions to the dispersionless Kadomtsev-Petviashvili equation. (English) Zbl 1486.65202 Lett. Math. Phys. 111, No. 5, Paper No. 113, 15 p. (2021). Reviewer: Anouar Ben Mabrouk (Monastir) MSC: 65M70 65M06 65T50 65N35 76L05 35Q53 PDFBibTeX XMLCite \textit{C. Klein} and \textit{N. Stoilov}, Lett. Math. Phys. 111, No. 5, Paper No. 113, 15 p. (2021; Zbl 1486.65202) Full Text: DOI
Klein, Christian; Nodari, Simona Rota On a nonlinear Schrödinger equation for nucleons in one space dimension. (English) Zbl 1476.35241 ESAIM, Math. Model. Numer. Anal. 55, No. 2, 409-427 (2021). MSC: 35Q55 35C08 65M70 81V35 PDFBibTeX XMLCite \textit{C. Klein} and \textit{S. R. Nodari}, ESAIM, Math. Model. Numer. Anal. 55, No. 2, 409--427 (2021; Zbl 1476.35241) Full Text: DOI arXiv
Crespo, S.; Fasondini, M.; Klein, C.; Stoilov, N.; Vallée, C. Multidomain spectral method for the Gauss hypergeometric function. (English) Zbl 1462.65092 Numer. Algorithms 84, No. 1, 1-35 (2020). MSC: 65L60 33C05 65D20 PDFBibTeX XMLCite \textit{S. Crespo} et al., Numer. Algorithms 84, No. 1, 1--35 (2020; Zbl 1462.65092) Full Text: DOI arXiv Link
Klein, Christian; McLaughlin, Ken; Stoilov, Nikola Spectral approach to the scattering map for the semi-classical defocusing Davey-Stewartson II equation. (English) Zbl 1453.37062 Physica D 400, Article ID 132126, 9 p. (2019). MSC: 37K35 65R20 65N35 35R30 PDFBibTeX XMLCite \textit{C. Klein} et al., Physica D 400, Article ID 132126, 9 p. (2019; Zbl 1453.37062) Full Text: DOI arXiv
Klein, Christian; Stoilov, Nikola Numerical scattering for the defocusing Davey-Stewartson II equation for initial data with compact support. (English) Zbl 1428.35520 Nonlinearity 32, No. 11, 4258-4280 (2019). MSC: 35Q55 65N35 65N80 35B40 37K15 PDFBibTeX XMLCite \textit{C. Klein} and \textit{N. Stoilov}, Nonlinearity 32, No. 11, 4258--4280 (2019; Zbl 1428.35520) Full Text: DOI arXiv
Klein, Christian; Stoilov, Nikola Numerical approach to Painlevé transcendents on unbounded domains. (English) Zbl 1397.34157 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 068, 10 p. (2018). MSC: 34M55 65L99 PDFBibTeX XMLCite \textit{C. Klein} and \textit{N. Stoilov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 068, 10 p. (2018; Zbl 1397.34157) Full Text: DOI arXiv
Frauendiener, Jörg; Klein, Christian Computational approach to compact Riemann surfaces. (English) Zbl 1360.14142 Nonlinearity 30, No. 1, 138-172 (2017). Reviewer: Noémie Combe (Marseille) MSC: 14Q05 14H45 14H70 14H10 PDFBibTeX XMLCite \textit{J. Frauendiener} and \textit{C. Klein}, Nonlinearity 30, No. 1, 138--172 (2017; Zbl 1360.14142) Full Text: DOI arXiv
Birem, Mira; Klein, Christian Multidomain spectral method for Schrödinger equations. (English) Zbl 1337.65129 Adv. Comput. Math. 42, No. 2, 395-423 (2016). MSC: 65M70 35Q55 PDFBibTeX XMLCite \textit{M. Birem} and \textit{C. Klein}, Adv. Comput. Math. 42, No. 2, 395--423 (2016; Zbl 1337.65129) Full Text: DOI arXiv
Grava, Tamara; Kapaev, Andrei; Klein, Christian On the tritronquée solutions of \(\mathrm{P}_{\mathrm{I}}^2\). (English) Zbl 1326.34136 Constr. Approx. 41, No. 3, 425-466 (2015). Reviewer: Sergei V. Rogosin (Minsk) MSC: 34M55 34E10 34M50 PDFBibTeX XMLCite \textit{T. Grava} et al., Constr. Approx. 41, No. 3, 425--466 (2015; Zbl 1326.34136) Full Text: DOI arXiv
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio On critical behaviour in systems of Hamiltonian partial differential equations. (English) Zbl 1321.35208 J. Nonlinear Sci. 25, No. 3, 631-707 (2015). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 37K05 34M55 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., J. Nonlinear Sci. 25, No. 3, 631--707 (2015; Zbl 1321.35208) Full Text: DOI arXiv
Frauendiener, Jörg; Klein, Christian Computational approach to hyperelliptic Riemann surfaces. (English) Zbl 1317.14127 Lett. Math. Phys. 105, No. 3, 379-400 (2015). Reviewer: Quentin Gendron (Frankfurt am Main) MSC: 14Q05 14H45 14H70 14H10 PDFBibTeX XMLCite \textit{J. Frauendiener} and \textit{C. Klein}, Lett. Math. Phys. 105, No. 3, 379--400 (2015; Zbl 1317.14127) Full Text: DOI arXiv Link
Klein, C.; Roidot, K. Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations. (English) Zbl 1291.35292 Physica D 265, 1-25 (2013). MSC: 35Q53 65T50 35B65 65M70 PDFBibTeX XMLCite \textit{C. Klein} and \textit{K. Roidot}, Physica D 265, 1--25 (2013; Zbl 1291.35292) Full Text: DOI arXiv
Grava, T.; Klein, C. A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions. (English) Zbl 1257.35165 Physica D 241, No. 23-24, 2246-2264 (2012). MSC: 35Q53 65M12 35B40 PDFBibTeX XMLCite \textit{T. Grava} and \textit{C. Klein}, Physica D 241, No. 23--24, 2246--2264 (2012; Zbl 1257.35165) Full Text: DOI arXiv
Frauendiener, Jörg; Klein, Christian; Shramchenko, Vasilisa Efficient computation of the branching structure of an algebraic curve. (English) Zbl 1238.14045 Comput. Methods Funct. Theory 11, No. 2, 527-546 (2011). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 14Q05 14H55 PDFBibTeX XMLCite \textit{J. Frauendiener} et al., Comput. Methods Funct. Theory 11, No. 2, 527--546 (2011; Zbl 1238.14045) Full Text: DOI arXiv
Frauendiener, Jörg; Klein, Christian Algebraic curves and Riemann surfaces in Matlab. (English) Zbl 1210.14070 Bobenko, Alexander I. (ed.) et al., Computational approach to Riemann surfaces. Berlin: Springer (ISBN 978-3-642-17412-4/pbk; 978-3-642-17413-1/ebook). Lecture Notes in Mathematics 2013, 125-162 (2011). MSC: 14Q05 14H50 PDFBibTeX XMLCite \textit{J. Frauendiener} and \textit{C. Klein}, Lect. Notes Math. 2013, 125--162 (2011; Zbl 1210.14070) Full Text: DOI
Dubrovin, B.; Grava, T.; Klein, C. On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation. (English) Zbl 1220.37048 J. Nonlinear Sci. 19, No. 1, 57-94 (2009). Reviewer: Bixiang Wang (Socorro) MSC: 37K05 35Q55 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., J. Nonlinear Sci. 19, No. 1, 57--94 (2009; Zbl 1220.37048) Full Text: DOI arXiv
Grava, Tamara; Klein, Christian Numerical solution of the small dispersion limit of Korteweg-de Vries and Whitham equations. (English) Zbl 1139.65069 Commun. Pure Appl. Math. 60, No. 11, 1623-1664 (2007). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M70 35B40 35Q53 PDFBibTeX XMLCite \textit{T. Grava} and \textit{C. Klein}, Commun. Pure Appl. Math. 60, No. 11, 1623--1664 (2007; Zbl 1139.65069) Full Text: DOI arXiv
Klein, Christian; Sparber, Christof; Markowich, Peter Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation. (English) Zbl 1128.37043 J. Nonlinear Sci. 17, No. 5, 429-470 (2007). MSC: 37K10 35Q53 34E05 35Q55 PDFBibTeX XMLCite \textit{C. Klein} et al., J. Nonlinear Sci. 17, No. 5, 429--470 (2007; Zbl 1128.37043) Full Text: DOI arXiv