On an Auxiliary Nonlinear Boundary Value Problem in the Ginzburg-Landau Theory of Superconductivity and its Multiple Solutions

Cover Page

Cite item


We realize analytic-numerical investigation of a homogeneous boundary value problem (BVP) for a second-order ordinary differential equation (ODE) with cubic nonlinearity and two real parameters which arises from the Ginzburg-Landau theory of superconductivity. Multiple nontrivial solutions to this problem depending on the specified parameters are expressed through the Jacobi elliptic functions and describe the stationary states (near the critical values of temperature) of a superconducting infinite plate of a finite thickness without magnetic field. It is a “degenerate” problem with respect to the original nonlinear BVP for a superconducting plate in a magnetic field and is important to construct algorithm for finding all the solutions to the indicated input problem in a wide range of the parameters. Studied problem is of separate mathematical interest by itself.

About the authors

N B Konyukhova


Email: nadja@ccas.ru

A A Sheina


Email: nadja@ccas.ru


Copyright (c) 2016 Конюхова Н.Б., Шеина А.А.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies