By the structure of solvable subgroup of <mml:math alttext="\[ SL\left( {2,\mathbb{C}} \right) \] " xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi><mml:mi>L</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>&#8450;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
 (see [1]), the integrability and
properties of solutions of a Riccati equation with an elliptic function coefficient, which is related to a
Fuchsian equation on the torus <mml:math alttext="\[ T^2  \] " xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>T</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>,is studied.

International Journal of Mathematics and Mathematical Sciences

Integrability of doubly-periodic Riccati equation

Abstract

Copyright