The application of trigonal curve theory to the second-order Benjamin-Ono hierarchy
The application of trigonal curve theory to the second-order Benjamin-Ono hierarchy
By introducing two sets of Lenard recursion equations, the second-order Benjamin-Ono hierarchy is proposed. In view of the characteristic polynomial of Lax matrix, a trigonal curve of arithmetic genus is deduced. Then the trigonal curve theory is used to derive the explicit algebro-geometric solutions represented in theta functions to the …