Haragus, Mariana; Johnson, Mathew A.; Perkins, Wesley R.; De Rijk, Björn Nonlinear modulational dynamics of spectrally stable Lugiato-Lefever periodic waves. (English) Zbl 1527.35048 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 40, No. 4, 769-802 (2023). Reviewer: Guido Schneider (Stuttgart) MSC: 35B35 35C07 35Q55 PDFBibTeX XMLCite \textit{M. Haragus} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 40, No. 4, 769--802 (2023; Zbl 1527.35048) Full Text: DOI arXiv
Johnson, Mathew A.; Perkins, Wesley R. Subharmonic dynamics of wave trains in the Korteweg-de Vries/Kuramoto-Sivashinsky equation. (English) Zbl 07776524 Stud. Appl. Math. 148, No. 3, 1274-1302 (2022). MSC: 35C07 35B35 35Q53 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{W. R. Perkins}, Stud. Appl. Math. 148, No. 3, 1274--1302 (2022; Zbl 07776524) Full Text: DOI arXiv
Johnson, Mathew A.; Perkins, Wesley R. Subharmonic dynamics of wave trains in reaction-diffusion systems. (English) Zbl 1491.37064 Physica D 422, Article ID 132891, 11 p. (2021). MSC: 37L15 35K57 35C07 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{W. R. Perkins}, Physica D 422, Article ID 132891, 11 p. (2021; Zbl 1491.37064) Full Text: DOI arXiv
Leisman, Katelyn Plaisier; Bronski, Jared C.; Johnson, Mathew A.; Marangell, Robert Stability of traveling wave solutions of nonlinear dispersive equations of NLS type. (English) Zbl 1467.35299 Arch. Ration. Mech. Anal. 240, No. 2, 927-969 (2021). MSC: 35Q55 35C07 35B10 35B20 65N25 PDFBibTeX XMLCite \textit{K. P. Leisman} et al., Arch. Ration. Mech. Anal. 240, No. 2, 927--969 (2021; Zbl 1467.35299) Full Text: DOI arXiv
Johnson, Mathew A.; Lyng, Gregory D.; Smith, Connor On the dynamics of traveling fronts arising in nanoscale pattern formation. (English) Zbl 1453.35023 Physica D 401, Article ID 132184, 16 p. (2020). MSC: 35B35 35C07 35B36 37N20 37M05 PDFBibTeX XMLCite \textit{M. A. Johnson} et al., Physica D 401, Article ID 132184, 16 p. (2020; Zbl 1453.35023) Full Text: DOI arXiv
Johnson, Mathew A.; Wright, J. Douglas Generalized solitary waves in the gravity-capillary Whitham equation. (English) Zbl 1454.35285 Stud. Appl. Math. 144, No. 1, 102-130 (2020). MSC: 35Q35 35C07 76B25 76B45 35B40 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{J. D. Wright}, Stud. Appl. Math. 144, No. 1, 102--130 (2020; Zbl 1454.35285) Full Text: DOI arXiv
Claassen, Kyle M.; Johnson, Mathew A. Numerical bifurcation and spectral stability of wavetrains in bidirectional Whitham models. (English) Zbl 1401.35250 Stud. Appl. Math. 141, No. 2, 205-246 (2018). MSC: 35Q35 35Q31 35C07 35C08 35B35 35B10 65N35 65H10 65F15 35B32 65P30 65L06 PDFBibTeX XMLCite \textit{K. M. Claassen} and \textit{M. A. Johnson}, Stud. Appl. Math. 141, No. 2, 205--246 (2018; Zbl 1401.35250) Full Text: DOI arXiv
Hur, Vera Mikyoung; Johnson, Mathew A. Modulational instability in the Whitham equation with surface tension and vorticity. (English) Zbl 1330.35329 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 129, 104-118 (2015). MSC: 35Q35 35C07 35Q53 35B35 76B15 76B45 76E20 PDFBibTeX XMLCite \textit{V. M. Hur} and \textit{M. A. Johnson}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 129, 104--118 (2015; Zbl 1330.35329) Full Text: DOI arXiv
Hur, Vera Mikyoung; Johnson, Mathew A. Stability of periodic traveling waves for nonlinear dispersive equations. (English) Zbl 1327.35032 SIAM J. Math. Anal. 47, No. 5, 3528-3554 (2015). MSC: 35B35 35Q53 35B10 35C07 PDFBibTeX XMLCite \textit{V. M. Hur} and \textit{M. A. Johnson}, SIAM J. Math. Anal. 47, No. 5, 3528--3554 (2015; Zbl 1327.35032) Full Text: DOI arXiv
Hur, Vera Mikyoung; Johnson, Mathew A. Modulational instability in the Whitham equation for water waves. (English) Zbl 1309.35079 Stud. Appl. Math. 134, No. 1, 120-143 (2015). MSC: 35Q35 76E30 76D33 76B15 35C07 35B10 PDFBibTeX XMLCite \textit{V. M. Hur} and \textit{M. A. Johnson}, Stud. Appl. Math. 134, No. 1, 120--143 (2015; Zbl 1309.35079) Full Text: DOI arXiv
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations. (English) Zbl 1304.35192 Invent. Math. 197, No. 1, 115-213 (2014). MSC: 35C07 35B40 35B10 35B35 35L65 35K55 PDFBibTeX XMLCite \textit{M. A. Johnson} et al., Invent. Math. 197, No. 1, 115--213 (2014; Zbl 1304.35192) Full Text: DOI arXiv
Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd An instability index theory for quadratic pencils and applications. (English) Zbl 1301.35081 Commun. Math. Phys. 327, No. 2, 521-550 (2014). Reviewer: Miloš Čanak (Beograd) MSC: 35P99 35C07 35Q53 PDFBibTeX XMLCite \textit{J. Bronski} et al., Commun. Math. Phys. 327, No. 2, 521--550 (2014; Zbl 1301.35081) Full Text: DOI arXiv
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation. (English) Zbl 1304.35184 Physica D 258, 11-46 (2013). MSC: 35C07 35B35 35K57 PDFBibTeX XMLCite \textit{B. Barker} et al., Physica D 258, 11--46 (2013; Zbl 1304.35184) Full Text: DOI arXiv
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin Nonlocalized modulation of periodic reaction diffusion waves: the Whitham equation. (English) Zbl 1270.35106 Arch. Ration. Mech. Anal. 207, No. 2, 669-692 (2013). Reviewer: Svetlin Georgiev (Rousse) MSC: 35B40 35C07 35B10 35K57 35B35 PDFBibTeX XMLCite \textit{M. A. Johnson} et al., Arch. Ration. Mech. Anal. 207, No. 2, 669--692 (2013; Zbl 1270.35106) Full Text: DOI arXiv
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin Nonlocalized modulation of periodic reaction diffusion waves: nonlinear stability. (English) Zbl 1276.35031 Arch. Ration. Mech. Anal. 207, No. 2, 693-715 (2013). Reviewer: Svetlin Georgiev (Rousse) MSC: 35B35 35K57 35C07 PDFBibTeX XMLCite \textit{M. A. Johnson} et al., Arch. Ration. Mech. Anal. 207, No. 2, 693--715 (2013; Zbl 1276.35031) Full Text: DOI arXiv
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin Stability of periodic Kuramoto-Sivashinsky waves. (English) Zbl 1238.35094 Appl. Math. Lett. 25, No. 5, 824-829 (2012). MSC: 35Q35 35B35 35C07 PDFBibTeX XMLCite \textit{B. Barker} et al., Appl. Math. Lett. 25, No. 5, 824--829 (2012; Zbl 1238.35094) Full Text: DOI arXiv
Bronski, Jared C.; Johnson, Mathew A.; Kapitula, Todd An index theorem for the stability of periodic travelling waves of Korteweg-de Vries type. (English) Zbl 1230.35118 Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 6, 1141-1173 (2011). MSC: 35Q53 35B35 35C07 35B10 PDFBibTeX XMLCite \textit{J. C. Bronski} et al., Proc. R. Soc. Edinb., Sect. A, Math. 141, No. 6, 1141--1173 (2011; Zbl 1230.35118) Full Text: DOI arXiv
Johnson, Mathew A.; Zumbrun, Kevin Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction-diffusion equations. (English) Zbl 1246.35034 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 4, 471-483 (2011). Reviewer: Jens Rademacher (Amsterdam) MSC: 35B35 35K57 37L15 35B10 35C07 35K45 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{K. Zumbrun}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 4, 471--483 (2011; Zbl 1246.35034) Full Text: DOI arXiv
Johnson, Mathew A.; Zumbrun, Kevin Nonlinear stability of periodic traveling-wave solutions of viscous conservation laws in dimensions one and two. (English) Zbl 1221.35055 SIAM J. Appl. Dyn. Syst. 10, No. 1, 189-211 (2011). Reviewer: Michael I. Gil’ (Beer-Sheva) MSC: 35B35 35C07 35K58 35L65 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{K. Zumbrun}, SIAM J. Appl. Dyn. Syst. 10, No. 1, 189--211 (2011; Zbl 1221.35055) Full Text: DOI arXiv
Johnson, Mathew A.; Zumbrun, Kevin Transverse instability of periodic traveling waves in the generalized Kadomtsev-Petviashvili equation. (English) Zbl 1233.35025 SIAM J. Math. Anal. 42, No. 6, 2681-2702 (2010). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35B35 35B10 35Q53 35C07 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{K. Zumbrun}, SIAM J. Math. Anal. 42, No. 6, 2681--2702 (2010; Zbl 1233.35025) Full Text: DOI arXiv
Johnson, M. A.; Zumbrun, K. Rigorous justification of the Whitham modulation equations for the generalized Korteweg-de Vries equation. (English) Zbl 1196.35184 Stud. Appl. Math. 125, No. 1, 69-89 (2010). MSC: 35Q53 35C07 35B35 81Q20 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{K. Zumbrun}, Stud. Appl. Math. 125, No. 1, 69--89 (2010; Zbl 1196.35184) Full Text: DOI arXiv
Johnson, Mathew A.; Zumbrun, Kevin Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case. (English) Zbl 1198.35027 J. Differ. Equations 249, No. 5, 1213-1240 (2010). MSC: 35B35 35C07 35B05 35L65 35L45 PDFBibTeX XMLCite \textit{M. A. Johnson} and \textit{K. Zumbrun}, J. Differ. Equations 249, No. 5, 1213--1240 (2010; Zbl 1198.35027) Full Text: DOI arXiv
Johnson, Mathew A. The transverse instability of periodic waves in Zakharov-Kuznetsov type equations. (English) Zbl 1190.35201 Stud. Appl. Math. 124, No. 4, 323-345 (2010). MSC: 35Q53 35B10 35B35 35C07 35C20 PDFBibTeX XMLCite \textit{M. A. Johnson}, Stud. Appl. Math. 124, No. 4, 323--345 (2010; Zbl 1190.35201) Full Text: DOI arXiv
Johnson, Mathew A. Nonlinear stability of periodic traveling wave solutions of the generalized Korteweg-de Vries equation. (English) Zbl 1200.35261 SIAM J. Math. Anal. 41, No. 5, 1921-1947 (2009). MSC: 35Q53 35B10 35B35 35C07 35A24 37K10 PDFBibTeX XMLCite \textit{M. A. Johnson}, SIAM J. Math. Anal. 41, No. 5, 1921--1947 (2009; Zbl 1200.35261) Full Text: DOI arXiv