Stanislavova, Milena; Stefanov, Atanas On the spectral problem \(\mathcal{L}u=\lambda u'\) and applications. (English) Zbl 1427.47010 Commun. Math. Phys. 343, No. 2, 361-391 (2016). MSC: 47A75 35B35 47N20 35C07 35Q53 PDF BibTeX XML Cite \textit{M. Stanislavova} and \textit{A. Stefanov}, Commun. Math. Phys. 343, No. 2, 361--391 (2016; Zbl 1427.47010) Full Text: DOI OpenURL
Chen, Chao-Nien; Choi, Y. S. Traveling pulse solutions to Fitzhugh-Nagumo equations. (English) Zbl 1328.34037 Calc. Var. Partial Differ. Equ. 54, No. 1, 1-45 (2015). Reviewer: Petr Tomiczek (Plzeň) MSC: 34C37 35K57 35C07 58E50 PDF BibTeX XML Cite \textit{C.-N. Chen} and \textit{Y. S. Choi}, Calc. Var. Partial Differ. Equ. 54, No. 1, 1--45 (2015; Zbl 1328.34037) Full Text: DOI OpenURL
Lanford, O. E. III.; Mintchev, S. M. Stability of a family of travelling wave solutions in a feedforward chain of phase oscillators. (English) Zbl 1316.34038 Nonlinearity 28, No. 1, 237-261 (2015). Reviewer: Carlo Laing (Auckland) MSC: 34C15 37C70 92C20 34A33 34D20 PDF BibTeX XML Cite \textit{O. E. III. Lanford} and \textit{S. M. Mintchev}, Nonlinearity 28, No. 1, 237--261 (2015; Zbl 1316.34038) Full Text: DOI OpenURL
Moore, Brian E.; Segal, Joseph M. Stationary bistable pulses in discrete inhomogeneous media. (English) Zbl 1283.39001 J. Difference Equ. Appl. 20, No. 1, 1-23 (2014). MSC: 39A10 39A12 34K21 39A30 PDF BibTeX XML Cite \textit{B. E. Moore} and \textit{J. M. Segal}, J. Difference Equ. Appl. 20, No. 1, 1--23 (2014; Zbl 1283.39001) Full Text: DOI OpenURL
Bellay, Jeremy; Scheel, Arnd Coherent structures near the boundary between excitable and oscillatory media. (English) Zbl 1191.37040 Dyn. Syst. 25, No. 1, 111-132 (2010). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37L10 35K57 37N25 37K45 37L15 PDF BibTeX XML Cite \textit{J. Bellay} and \textit{A. Scheel}, Dyn. Syst. 25, No. 1, 111--132 (2010; Zbl 1191.37040) Full Text: DOI Link OpenURL
Kaushik, Aditya Singular perturbation analysis of bistable differential equation arising in the nerve pulse propagation. (English) Zbl 1156.35400 Nonlinear Anal., Real World Appl. 9, No. 5, 2106-2127 (2008). MSC: 35K55 92C50 35B25 65M06 65M12 65M15 PDF BibTeX XML Cite \textit{A. Kaushik}, Nonlinear Anal., Real World Appl. 9, No. 5, 2106--2127 (2008; Zbl 1156.35400) Full Text: DOI OpenURL
van Heijster, Peter; Doelman, Arjen; Kaper, Tasso J. Pulse dynamics in a three-component system: Stability and bifurcations. (English) Zbl 1153.37437 Physica D 237, No. 24, 3335-3368 (2008). MSC: 37L10 37L15 35K57 35B32 35B35 PDF BibTeX XML Cite \textit{P. van Heijster} et al., Physica D 237, No. 24, 3335--3368 (2008; Zbl 1153.37437) Full Text: DOI OpenURL
Dkhil, F.; Logak, E.; Nishiura, Y. Some analytical results on the Gray-Scott model. (English) Zbl 1071.35062 Asymptotic Anal. 39, No. 3-4, 225-261 (2004). MSC: 35K40 35K55 35K57 PDF BibTeX XML Cite \textit{F. Dkhil} et al., Asymptotic Anal. 39, No. 3--4, 225--261 (2004; Zbl 1071.35062) OpenURL
Leach, J. A.; Wei, J. C. Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I: Stability analysis. (English) Zbl 1027.80010 Physica D 180, No. 3-4, 185-209 (2003). MSC: 80A30 35B35 PDF BibTeX XML Cite \textit{J. A. Leach} and \textit{J. C. Wei}, Physica D 180, No. 3--4, 185--209 (2003; Zbl 1027.80010) Full Text: DOI OpenURL
Hood, A. W.; Brooks, S. J.; Wright, A. N. Coronal heating by the phase mixing of individual pulses propagating in coronal holes. (English) Zbl 1009.85005 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2026, 2307-2325 (2002). MSC: 85A15 PDF BibTeX XML Cite \textit{A. W. Hood} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 458, No. 2026, 2307--2325 (2002; Zbl 1009.85005) Full Text: DOI OpenURL
Afendikov, Andrei L.; Bridges, Thomas J. Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow. (English) Zbl 0984.76022 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 457, No. 2006, 257-272 (2001). MSC: 76E05 PDF BibTeX XML Cite \textit{A. L. Afendikov} and \textit{T. J. Bridges}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 457, No. 2006, 257--272 (2001; Zbl 0984.76022) Full Text: DOI Link OpenURL
Ewodo, J. Ndzié Behavior of time-reversed pulses in random media. (English) Zbl 0972.60103 Stochastic Anal. Appl. 19, No. 1, 45-57 (2001). MSC: 60K37 60H15 PDF BibTeX XML Cite \textit{J. N. Ewodo}, Stochastic Anal. Appl. 19, No. 1, 45--57 (2001; Zbl 0972.60103) Full Text: DOI OpenURL
Nii, Shunsaku A topological approach to stability of pulses bifurcating from an inclination-flip homoclinic orbit. (English) Zbl 0983.35062 Methods Appl. Anal. 7, No. 1, 205-231 (2000). Reviewer: Alois Steindl (Wien) MSC: 35K57 35B35 35B32 PDF BibTeX XML Cite \textit{S. Nii}, Methods Appl. Anal. 7, No. 1, 205--231 (2000; Zbl 0983.35062) Full Text: DOI OpenURL
Ikeda, Tsutomu; Ikeda, Hideo; Mimura, Masayasu Hopf bifurcation of travelling pulses in some bistable reaction-diffusion systems. (English) Zbl 0982.35049 Methods Appl. Anal. 7, No. 1, 165-193 (2000). Reviewer: Aois Steindl (Wien) MSC: 35K57 35B32 35B10 35B35 35B25 PDF BibTeX XML Cite \textit{T. Ikeda} et al., Methods Appl. Anal. 7, No. 1, 165--193 (2000; Zbl 0982.35049) Full Text: DOI OpenURL
Mimura, Masayasu; Nagayama, Masaharu; Ikeda, Hideo; Ikeda, Tsutomu Dynamics of travelling breathers arising in reaction-diffusion systems (ODE modelling approach). (English) Zbl 1003.65116 Hiroshima Math. J. 30, No. 2, 221-256 (2000). MSC: 65M70 65M12 35B25 35B32 35K57 PDF BibTeX XML Cite \textit{M. Mimura} et al., Hiroshima Math. J. 30, No. 2, 221--256 (2000; Zbl 1003.65116) OpenURL
Ikeda, Hideo; Ikeda, Tsutomu Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems. (English) Zbl 0949.34030 J. Dyn. Differ. Equations 12, No. 1, 117-167 (2000). MSC: 34C23 34C60 34E15 34B15 35K57 PDF BibTeX XML Cite \textit{H. Ikeda} and \textit{T. Ikeda}, J. Dyn. Differ. Equations 12, No. 1, 117--167 (2000; Zbl 0949.34030) Full Text: DOI OpenURL
Chen, Liping Character as solitary wave in a certain one-dimensional array. (Chinese. English summary) Zbl 0976.34044 Acta Math. Sci. (Chin. Ed.) 19, No. 4, 361-367 (1999). MSC: 34D10 34C37 PDF BibTeX XML Cite \textit{L. Chen}, Acta Math. Sci. (Chin. Ed.) 19, No. 4, 361--367 (1999; Zbl 0976.34044) OpenURL
Bressloff, P. C.; Coombes, S. Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays. (English) Zbl 0937.34060 Physica D 126, No. 1-2, 99-122 (1999). MSC: 34K20 34C15 34K13 PDF BibTeX XML Cite \textit{P. C. Bressloff} and \textit{S. Coombes}, Physica D 126, No. 1--2, 99--122 (1999; Zbl 0937.34060) Full Text: DOI OpenURL
Bressloff, P. C.; Coombes, S. Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays. (English) Zbl 0934.34057 Physica D 130, No. 3-4, 232-254 (1999). MSC: 34K10 34C15 92B05 82D55 34K11 PDF BibTeX XML Cite \textit{P. C. Bressloff} and \textit{S. Coombes}, Physica D 130, No. 3--4, 232--254 (1999; Zbl 0934.34057) Full Text: DOI OpenURL
Kawaguchi, Satoshi; Mimura, Masayasu Collision of travelling waves in a reaction-diffusion system with global coupling effect. (English) Zbl 0936.35089 SIAM J. Appl. Math. 59, No. 3, 920-941 (1999). Reviewer: Georgii Sviridyuk (Chelyabinsk) MSC: 35K57 35B25 35B32 PDF BibTeX XML Cite \textit{S. Kawaguchi} and \textit{M. Mimura}, SIAM J. Appl. Math. 59, No. 3, 920--941 (1999; Zbl 0936.35089) Full Text: DOI OpenURL
Chen, Xinfu; Hastings, Stuart P. Pulse waves for a semi-discrete Morris-Lecar type model. (English) Zbl 0972.92007 J. Math. Biol. 38, No. 1, 1-20 (1999). Reviewer: Tanya Kostova-Vassilevska (San Ramon) MSC: 92C20 37N25 34K99 PDF BibTeX XML Cite \textit{X. Chen} and \textit{S. P. Hastings}, J. Math. Biol. 38, No. 1, 1--20 (1999; Zbl 0972.92007) Full Text: DOI OpenURL
Doelman, Arjen; Kaper, Tasso J.; Zegeling, Paul A. Pattern formation in the one-dimensional Gray-Scott model. (English) Zbl 0905.35044 Nonlinearity 10, No. 2, 523-563 (1997). MSC: 35K57 34C37 35B10 35B32 35Q80 34E15 65M06 34C30 PDF BibTeX XML Cite \textit{A. Doelman} et al., Nonlinearity 10, No. 2, 523--563 (1997; Zbl 0905.35044) Full Text: DOI Link OpenURL
Gordon, Michael S.; Shearer, Michael; Schaeffer, David Plane shear waves in a fully saturated granular medium with velocity and stress controlled boundary conditions. (English) Zbl 0890.73017 Int. J. Non-Linear Mech. 32, No. 3, 489-503 (1997). MSC: 74J10 74J99 PDF BibTeX XML Cite \textit{M. S. Gordon} et al., Int. J. Non-Linear Mech. 32, No. 3, 489--503 (1997; Zbl 0890.73017) Full Text: DOI OpenURL
Bose, Amitabha Symmetric and antisymmetric pulses in parallel coupled nerve fibres. (English) Zbl 0836.34055 SIAM J. Appl. Math. 55, No. 6, 1650-1674 (1995). MSC: 34E15 34C37 34D15 35K57 PDF BibTeX XML Cite \textit{A. Bose}, SIAM J. Appl. Math. 55, No. 6, 1650--1674 (1995; Zbl 0836.34055) Full Text: DOI OpenURL
Herrero, Henar; Riecke, Hermann Front structures in a real Ginzburg-Landau equation coupled to a mean field. (English) Zbl 0879.76034 Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, No. 5, 1343-1346 (1994). MSC: 76E15 35Q35 PDF BibTeX XML Cite \textit{H. Herrero} and \textit{H. Riecke}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, No. 5, 1343--1346 (1994; Zbl 0879.76034) Full Text: DOI OpenURL
Kuznetsov, Yu. A. Pulses of complicated shape in models of nerve conduction. (English. Russian original) Zbl 0798.92008 Bazykin, A. (ed.) et al., Mathematics and modelling. Commack, NY: Nova Science Publishers, Inc.. 299-320 (1993); translation from Mathematics and modeling, Collect Sci. Works, Pushchino, 208-222 (1990). Reviewer: T.Kostova-Vassilevska (Sofia) MSC: 92C20 35Q92 35B32 35K57 PDF BibTeX XML Cite \textit{Yu. A. Kuznetsov}, in: Mathematics and modelling. Commack, NY: Nova Science Publishers, Inc.. 299--320 (1993; Zbl 0798.92008); translation from Mathematics and modeling, Collect Sci. Works, Pushchino, 208--222 (1990) OpenURL
Kopell, N. Dynamical systems and the geometry of singularly perturbed differential equations. (English) Zbl 0799.34059 Hirsch, M. W. (ed.) et al., From topology to computation: Proceedings of the Smalefest. Papers presented at the conference “From topology to computation: Unity and diversity in the mathematical sciences” held at the University of California at Berkeley, USA, August 5-9, 1990 in honor of Stephen Smale’s 60th birthday. New York: Springer-Verlag. 545-556 (1993). Reviewer: M.Rodriguez Ricard (La Habana) MSC: 34E15 37J40 34C37 PDF BibTeX XML Cite \textit{N. Kopell}, in: From topology to computation: Proceedings of the Smalefest. Papers presented at the conference ''From topology to computation: Unity and diversity in the mathematical sciences'' held at the University of California at Berkeley, USA, August 5-9, 1990 in honor of Stephen Smale's 60th birthday. New York: Springer-Verlag. 545--556 (1993; Zbl 0799.34059) OpenURL
Sneyd, James; Girard, Steven; Clapham, David Calcium wave propagation by calcium-induced calcium release: An unusual excitable system. (English) Zbl 0758.92007 Bull. Math. Biol. 55, No. 2, 315-344 (1993). MSC: 92C30 PDF BibTeX XML Cite \textit{J. Sneyd} et al., Bull. Math. Biol. 55, No. 2, 315--344 (1993; Zbl 0758.92007) Full Text: DOI OpenURL
Engelbrecht, Juri; Fusco, Domenico; Oliveri, Francesco Nerve pulse transmission: Recovery variable and rate-type effects. (English) Zbl 0783.92007 Chaos Solitons Fractals 2, No. 2, 197-209 (1992). Reviewer: T.Kostova-Vassilevska (Los Angeles) MSC: 92C20 74D99 74Hxx PDF BibTeX XML Cite \textit{J. Engelbrecht} et al., Chaos Solitons Fractals 2, No. 2, 197--209 (1992; Zbl 0783.92007) Full Text: DOI OpenURL
Engelbrecht, J. An introduction to asymmetric solitary waves. (English) Zbl 0745.35038 Pitman Monographs and Surveys in Pure and Applied Mathematics. 56. Harlow, New York etc.: Longman Scientific & Technical, John Wiley & Sons. 280 p. (1991). Reviewer: Wang Cun-Zheng (Chengdu) MSC: 35Q53 35Q51 35-02 76B25 92C20 PDF BibTeX XML Cite \textit{J. Engelbrecht}, An introduction to asymmetric solitary waves. Harlow: Longman Scientific \&| Technical; New York etc.: John Wiley \&| Sons (1991; Zbl 0745.35038) OpenURL
Tsujikawa, T. Singular perturbation approach to stability of traveling pulse solutions of the FitzHugh-Nagumo equations. (English) Zbl 0688.35040 Boundary and interior layers - computational and asymptotic methods, Proc. 5th Int. Conf., BAIL-V, Shanghai/China 1988, Conf. Ser. 12, 357-362 (1988). MSC: 35K60 35B25 47D03 35B35 65M99 65N99 PDF BibTeX XML OpenURL
Bates, Peter W.; Jones, Christopher K. R. T. Invariant manifold theorems with applications. (English) Zbl 0604.58033 Nonlinear functional analysis and its applications, Proc. NATO Adv. Study Inst., Maratea/Italy 1985, NATO ASI Ser., Ser. C 173, 177-186 (1986). Reviewer: J.Marschall MSC: 37C75 PDF BibTeX XML OpenURL
Yanagida, Eiji Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations. (English) Zbl 0566.92009 J. Math. Biol. 22, 81-104 (1985). Reviewer: T.Kostova-Vassilevska MSC: 92Cxx 35B35 35P99 PDF BibTeX XML Cite \textit{E. Yanagida}, J. Math. Biol. 22, 81--104 (1985; Zbl 0566.92009) Full Text: DOI OpenURL
Pauwelussen, J. P. Nerve impulse propagation in a branching nerve system: A simple model. (English) Zbl 0429.92012 Math. Cent., Amst., Afd. Toegepaste Wiskd. 203, 52 P. (1980). MSC: 92Cxx 35K15 35B35 35K55 35B30 PDF BibTeX XML OpenURL