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Referencias:

• Amster, P., Kwong, M.K., Rogers, C., A Painlevé II model in two-ion electro diffusion with radiation boundary conditions (2014) Nonlinear Analysis: Real World Applications, 16, pp. 120-131
• Amster, P., Kwong, M.K., Rogers, C., A Neumann boundary value problem in two-ion electro-diffusion with unequal valencies (2012) Discrete and Continuous Dynamical Systems, 17, pp. 2299-2311
• Amster, P., Kwong, M.K., Rogers, C., On a Neumann boundary value problem for the Painlevé II equation in two-ion electro-diffusion (2011) Nonlinear Analysis, 74, pp. 2897-2907
• Amster, P., Mariani, M.C., Rogers, C., Tisdell, C.C., On two-point boundary value problems in multi-ion electrodiffusion (2004) J. Math. Anal. Appl., 289, pp. 712-721
• Amster, P., Rogers, C., On boundary value problems in three-ion electrodiffusion (2007) J. Math. Anal. Appl., 333, pp. 42-51
• Amster, P., Vicchi, L., Rogers, C., Boundary value problems on the half-line for a generalised Painlevé II equation (2009) Nonlinear Analysis, 71, pp. 149-154
• Bass, L., Irreversible interactions between metals and electrolytes (1964) Proc. Roy. Soc. Lond. A, 277, pp. 125-136
• Bass, L., Electric structures of interfaces in steady electrolysis (1964) Trans. Faraday Soc., 60, pp. 1656-1663
• Bass, L., Nimmo, J., Rogers, C., Schief, W.K., Electrical structures of interfaces. A Painlevé II model (2010) Proc. Roy. Soc. London A, 466, pp. 2117-2136
• De Boer, P.C.T., Ludford, G.S.S., Spherical electric probe in a continuum gas (1975) Plasma Phys., 17, pp. 29-43
• O'Bokris, J.M., Reddy, A.K.N., (1970) Modern Electrochemistry, , Plenum, New York
• Bracken, A.J., Bass, L., Rogers, C., Bäcklund flux-quantization in a model of electrodiffusion based on Painlevé II (2012) J. Phys. A: Math.&Theor., 45, p. 105204. , 20pp
• Cole, K.S., (1968) Membranes, Ions and Impulses, , University of California Press, Berkeley
• Conte, R., Rogers, C., Schief, W.K., Painlevé structure of a multi-ion electrodiffusion system (2007) J. Phys. A: Math. Theor., 40, pp. F1031-F1040
• De Coster, C., Habets, P., (2006) Two-Point Boundary Value Problems: Lower and Upper Solu-tions, , Mathematics in Science and Engineering, 205 Elsevier, Amsterdam
• Hägglund, J.V., Single-ion electrodiffusion models of the late sodium and potassium currents in the giant axon of the squid (1972) J. Membrane Biol, 10, pp. 153-170
• Hastings, S.P., McLeod, J.B., A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation (1980) Arch. Rat. Mech. Anal., 73, pp. 31-51
• Grafov, B.M., Chernenko, A.A., Theory of the passage of a constant current through a solution of a binary electrolyte (1962) Dokl. Akad. Navk. SSR, 146, pp. 135-138
• Gromak, V.I., Bäcklund transformations of Painlevé equations and their applications (1999) The Painlevé Property. One Century Later, pp. 687-734. , (Ed. R. Conte), CRM Series in Mathematical Physics, Springer Verlag, New York
• Heiffer, B., Weissler, F.B., On a family of solutions of the second Painlevé equation related to superconductivity (1998) Eur. J. Appl. Math., 9, pp. 223-243
• Holmes, P., Spence, D., On a Painlevé-type boundary value problem (1984) Quart. J. Mech. Appl. Math., 37, pp. 525-538
• Kudryashov, N.A., The second Painlevé equation as a model for the electric field in a semiconductor (1997) Phys. Lett. A, 233, pp. 397-400
• Lee, J.H., Pashaev, O.K., Rogers, C., Schief, W.K., The resonant nonlinear Schrödinger equation in cold plasma physics. Application of Bäcklund-Darboux transformations and superposition principles (2007) J. Plasma Phys., 73, pp. 257-272
• Leuchtag, H.R., A family of differential equations arising from multi-ion electro-diffusion (1981) J. Math. Phys., 22, pp. 1317-1320
• Leuchtag, H.R., Swihart, J.C., Steady state electrodiffusion. Scaling, exact solution for ions of one charge, and the phase plane (1977) Biophys. J., 17, pp. 27-46
• Mackey, M.C., Admittance properties of electrodiffusion membrane models (1975) Math. Biosci., 25, pp. 67-80
• Mariani, M.C., Amster, P., Rogers, C., Dirichlet and periodic-type boundary value problems for Painlevé II (2002) J. Math. Anal. Appl., 265, pp. 1-11
• Nernst, W., Zur Kinetik der in Lösung befindlichen Körper. Erste Abhandlung. Theorie der Diffusion (1888) Z. Phys. Chem., 2, pp. 613-637
• Pashaev, O.K., Lee, J.H., Resonance solitons as black holes in Madelung fluid (2002) Mod. Phys. Lett. A, 17, pp. 1601-1619
• Planck, M., Über die Erregung von Elektricität und Wärme in Electrolyten (1890) Ann. Phys. Chem., 39, pp. 161-186
• Ray, J.R., Nonlinear superposition law for generalised Ermakov systems (1980) Phys. Lett. A, 78, pp. 4-6
• Reid, J.L., Ray, J.R., Ermakov systems, nonlinear superposition and solution of nonlinear equations of motion (1980) J. Math. Phys., 21, pp. 1583-1587
• Rogers, C., A novel Ermakov-Painlevé II system. N +1-dimensional coupled NLS and elastodynamic reductions (2014) Stud. Appl. Math., 133, pp. 214-231
• Rogers, C., An, H., Ermakov-Ray-Reid systems in 2+1-dimensional rotating shallow water theory (2010) Stud. Appl. Math., 125, pp. 275-299
• Rogers, C., Bassom, A., Schief, W.K., On a Painlevé II model in steady electrolysis: Application of a Bäcklund transformation (1999) J. Math. Anal. Appl., 240, pp. 367-381
• Rogers, C., Hoenselaers, C., Ray, J.R., On 2 + 1-dimensional Ermakov systems (1993) J. Phys. A: Math. Gen., 26, pp. 2625-2633
• Rogers, C., Malomed, B., An, H., Ermakov-Ray-Reid reductions of variational approximations in nonlinear optics (2012) Stud. Appl. Math., 129, pp. 389-413
• Rogers, C., Schief, W.K., Multi-component Ermakov systems: Structure and linearization (1996) J. Math. Anal. Appl., 198, pp. 194-220
• Rogers, C., Schief, W.K., Winternitz, P., Lie theoretical generalization and discretisation of the Pinney equation (1997) J. Math. Anal. Appl., 216, pp. 246-264
• Sandblom, J., Anomalous reactances in electrodiffusion systems (1972) Biophys. J., 12, pp. 1118-1130
• Schief, W.K., Rogers, C., Bassom, A., Ermakov systems with arbitrary order and dimension. Structure and linearization (1996) J. Phys. A: Math. Gen., 29, pp. 903-911
• Schlögl, R., Elektrodiffusion in freier Lösung und geladenen Membranen (1954) Z. Physik. Chem. Neue Folge, 1, pp. 305-339
• Schwarz, T.L., (1971) Biophysics and Physiology of Excitable Membranes, , W.J. Adelman Jr. (Ed.), Van Rostrand, New York
• Thompson, H.B., Existence of solutions for a two point boundary value problem arising in electro-diffusion (1988) Acta. Math. Sci., 8, pp. 373-387
• Thompson, H.B., Existence for two-point boundary value problems in two ion electro diffusion (1994) Journal of Mathematical Analysis and Applications, 184, pp. 82-94

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