Lame Potential Research Articles

On elliptic string solutions in AdS3 and dS3

Classical string actions in AdS(3) and dS(3) can be connected to the sinh-Gordon and cosh-Gordon equations through Pohlmeyer reduction. We show that the problem of constructing a classical string solution with a given static or translationally invariant Pohlmeyer counterpart is equivalent to solving four pairs of effective Schrodinger problems. Each pair consists of a flat potential and an n = 1 Lame potential whose eigenvalues are connected, and, additionally, the four solutions satisfy a set of constraints. An approach for solving this system is developed by employing an interesting connection between the specific class of classical string solutions and the band structure of the Lame potential. This method is used for the construction of several families of classical string solutions, one of which turns out to be the spiky strings in AdS(3). New solutions include circular rotating strings in AdS(3) with singular time evolution of their radius and angular velocity as well as classical string solutions in dS(3).

Symmetric monopoles and finite-gap Lamé potentials

For each positive integer g, we construct a one-parameter family of spectral curves for D-2 symmetric charge 2g + 1 SU(2) BPS monopoles. Each spectral curve is reducible, and is the union of a line with g elliptic curves. We show that such a monopole is related to a g-gap Lame potential. Other symmetric monopoles. related to elliptic curves, are also shown to have a similar correspondence. A suggestion is made on how this observation may be of use in the construction of new spectral curves.

On the two-gap elliptic potentials

Theτ-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<τ<1, (ii) for rational values ofτ such potentials are elliptic (i.e., double-periodic), (iii) within the limitτ→0 this family degenerates to the soliton potential, (iv) within the limitτ→1 this family degenerates to the one-gap Lame potential.

Lam�-type potentials in a non-Newtonian fluid theory

The existence and completeness of a set of potentials are exhibited in the case of a linear system of coupled differential equations characterizing slow incompressible flow of micropolar fluids. These potentials correspond to the Lame's potential of classical elasticity.