Rational solutions of the Noumi and Yamada system of type A4(1)

Article Outline

1. INTRODUCTION
2. MEROMORPHIC SOLUTIONS AT t = ∞
   1. The case where f _i  (0 ⩽ i ⩽ 4) are all holomorphic at t = ∞
   2. The case where one of f _i  (0 ⩽ i ⩽ 4) has a pole at t = ∞
   3. The case where two of f _i   (0 ⩽ i ⩽ 4) have a pole at t = ∞
      1. The case where f _i , f _i+1 have a pole at t = ∞
      2. The case where f _i , f _i+2 have a pole at t = ∞
   4. The case where three of f _i   (0 ⩽ i ⩽ 4) have a pole at t = ∞
      1. The case where f _i , f _i+1 , f _i+2 have a pole at t = ∞
      2. The case where f _i , f _i+1 , f _i+3 have a pole at t = ∞
   5. The case where four of f _i  (0 ⩽ i ⩽ 4) have a pole at t = ∞
   6. The case where all of f _i  (0 ⩽ i ⩽ 4) have a pole at t = ∞
   7. Summary
3. MEROMORPHIC SOLUTIONS AT t = c∈
4. THE LAURENT SERIES OF THE AUXILIARY FUNCTION
   1. The Laurent series of at t = ∞
   2. The Laurent series of at t = c∈
   3. Rational solutions and the residue calculus of
5. NECESSARY CONDITIONS
   1. Necessary conditions for Type A
   2. Necessary condition for Type B
   3. Necessary condition for Type C
6. REDUCTION OF THE PARAMETERS
   1. Shift operators
   2. The reduction of the parameters for Type A
   3. Reduction of the parameters for Type B
   4. Reduction of the parameters for Type C
7. RATIONAL SOLUTIONS FOR SOME PARAMETERS
   1. Rational solutions of A4(1)(1,0,0,0,0)
   2. Rational solutions of Type B for some parameters
   3. Rational solutions of Type C for some parameters
8. PROOF OF MAIN THEOREM
   1. Main theorem for Type A
   2. Main theorem for Type B
   3. Main theorem for Type C