An h-dependent formulation of the Kadomtsev-Petviashvili hierarchy

作者：Takasaki K^*; Takebe T

来源：Theoretical and Mathematical Physics, 2012, 171(2): 683-690.

DOI：10.1007/s11232-012-0065-y

• (h)over-bar-expansion
• Riemann-Hilbert problem
• quantization
• recurrence relation

We briefly review a recursive construction of A -dependent solutions of the Kadomtsev-Petviashvili hierarchy. We give recurrence relations for the coefficients X-n of an A -expansion of the operator X = X (0) + A X (1) + A (2) X (2) + ... for which the dressing operator W is expressed in the exponential form W = e(X/A ). The wave function I associated with W turns out to have the WKB (Wentzel-Kramers-Brillouin) form I = e(S/kh), and the coefficients S-n of the A -expansion S = S (0) + A S (1) + A (2) S (2) + ... are also determined by a set of recurrence relations. We use this WKB form to show that the associated tau function has an A -expansion of the form log tau = A (-2) F (0) + A (-1) F (1) + F (2) + ....

• 出版日期2012-5