“指数”SG方程的Backlund变换.pdf

36 6 o Vol.36, No. 6 1993 m 11 E ACTA MATHEMATICA SINICA Nov., 1993 yo SG W Z B¨acklund Tc
z (Tckr 830035) w u [1]   T ,  T  AKNS  (1)   (10),  (10)  uxt = C (t)enu  Lax  Ω[1],[2],  uxt = C (t)enu  !#$! B¨acklund (14), %()* afY+, SG   B¨acklund v ANKS X dΩ − Ω ∧ Ω = 0 ibgr pmieqX ω1 + dα − sh(α + λ)ω2 − ch(α − λ)ω12 = 0 y  n −n ux   C (t)enu C (t)enu  4 2 Ω =  −n ux −n  dx +  C (t)enu −C (t)enu  dt, 2 4 pM n ∈ N, u = u(x, t), GVSj SL(2) WA dΩ − Ω ∧ Ω = 0 (1) I uxt = C (t)enu , (2) (2) AKNS z AKNS C Gauss xe K = −1 xhJPC OMq I = ω2 + ω2 K = −1 xh 1 2 dω1 = ω12 ∧ ω2 , dω2 = −ω12 ∧ ω1, dω12 = ω1 ∧ ω2 . (3) b  − 1ω2 1 (ω1 + ω12)  2 2 Ω = Ωij =  1 (ω1 − ω12) 1ω2  , (4) 2 2 1987 - 11 . 13 /01 1993 -3 .23 /23456 844 36 G Ω fP AKNS (1). J Ω fP (1), G (4) ω , ω , ω fP (3), 1 2 12 K = −1 xh (4) l j 1 (4) ZxSjJ  ch α sh α 