【正文】 20240)2(22)4(2220)2(22039???????????eahaahaahaebebaaeabaF 40 .,4,021412402242024021431aabbababababhhhbbaaa??????????????? ).0(,)( )( 422)(1)2(0)4(24 2)2(2)(10)2(240 ???? ???? ?? ???? baaeaeaeab aeaeaaeaF ??? ??? 41 .16,0 ,0240212 10431221 ?????? ????????? ??? hhhbbb bbaaaaaa ).0(,404)4(041 ??? babeaF? 42 .25,0 ,0240212 10432210 ?????? ????????? ?? hhhbbb bbaaaaaa ).0(,414)5(142 ?? ??? babeaF? 43 .,9,042112402110243210bbaahhhbbbbaaaaaa?????????????????? ).0(,)( )( 412)2(44)2()(2)(4143 ?????? babebb eebebaF ???? 紅河學院本科畢業(yè)論文（設計） 9 44 .36,9,042142202110431220bahbhhbbbbaaaaaa?????????????????? .3636)2(214)4(24)(4144?????? eahebebaF 45 .,16,02420240211043211bbaahhhbbbbaaaaa????????????????? ).0(,)()(222)2(42)2()2(24245 ???????? babebbeebbaF??? 46 .36,0 24022 110431210 ?????? ????????? ?? hhhbb bbbaaaaaa ).0(,424)6(246 ?? ??? babeaF? 47 .,9,0211421122402104320?????????????????ababababhhhbbbaaaa ).0(,)( )( 122)(1)3(11)()2(2)(1)(1247 ??? ??? ????????? baaeaeab eeaeaeaaF ?????? 48 .4,1,042342202110421210bahbhhbbbbaaaaaa?????????????????? .)s i n h (2.44434848443234)2(24)(4348???haFFhbaahebebaF??????? 成為時，當 49 .)(4,)(,1,023234144332341102021142201abababhababaabhhbbbaaaaa????????????????? ???? .))c o s h ()( s i n h (.43494931422341)2(32)(2349????????????baFFaabbbabaeab eaF成為時，當 50 .1,02324131403142304140242??????????????haabbaabba abba abbhhbaa /)( )(2)(10)(1)3(3350 ???? ???? ????? eaeaaeaeaaF).0() ) ,(( 43)(21)(0)2(13)4(4 ????? ??? baeaaeaeaaeb ???? 51 .36,9,042102244212032101abhahhbbbbbaaaaa?????????????????? ).0(,36 )36( 1414)()2(210)4(2451 ????? baba eebheaF??? 52 .25,0 24042 120322101 ?????? ???????? ??? hhhbb bbbaaaaaa ).0(, 141 )5(452 ?? ?? babeaF ? 53 .36,0 24042 110322101 ?????? ???????? ??? hhhbb bbbaaaaaa ).0(,242)6(453 ?? ?? babeaF? 第二 章 Benjamin Ono 方程的精確解 10 54 .,16,4,02002204222040244121311bbaabbaabaahhhbbbbaaa?????????????????? /)()2(0020)2(04)4(2454 ??? ????? ebabaebaebaF).( 0)2(22 bebb ?? 55 .9,9,18,0242444242242402210132101abhbbaabahhbbbbaaaaa??????????????????? ).0(,)()(44)2(2)4(44)4(4)2(2455 ???????? baebebbebebaF???? 56 .425,425,225,0242444141242402221032102abhbbaabahhbbbbaaaaa??????????????????? ).0(,)( )( 44)(1)4(44 )(1)4(4456 ???? ?? ?? baebebb ebebaF ?? ?? 57 .,16,4,01234121021130241240212bbaabbaabaahhhbbbbaaa??????????????????? .)( )(1)(21)()(1121)3(13)4(2357 bebb eebabaebaebaF ? ????????????? 58 .,9,00134240421221021bbaahhhbbbbaaaaa????????????? ???? ).0(,030)3(358 ?? babeaF? 59 .,16,0,0024201432404211021bbaabbaahhhbbbaaaa???????????????? ).0(,)( )( 04)2(2)(100)2(2)3(1)4(0459 ??? ??? ???? ?? baebebb ebebebaF ????? 60 .,25,0,02134240421021021?????????????????bbaahhhbbbbaaaaa ).0(,)()(23)(212)()3(2)4(1360 ??????????? baebbeebebaF???? 61 .,4 2 134240421 ? ??? ??????? b baahhhbaa )( )( )2(2)(10)(1)2(22)2(2)(1)2(0)3(1)4(2461 ???????????????????? ???? ebebbebebb ebebebebebaF).0(, 24 ?ba Benjamin Ono 方程的求解及對解的變換和分析 Benjamin Ono 方程的 一般解 為 求 (11)方程的 一般解 ，作 行波 變換 紅河學院本科畢業(yè)論文（設計） 11 ,),(),( btaxutxu ??? ?? (29) 其中 ,ab為待定常數，將 (29)式帶入 (11)式， 可將 (11)式的左端化為關于 ()u?的 ODE ,0))((2 222)4(4 ????????? uuuaubua ?? (210) 其中 (4),u u u? ? 分別表示 u 對 ? 求四階、一階、 二階導數 .由方程 (210)中 的非線性項 uu?? 和最高階導數項 (4)u 齊次平衡，得 2n? .故可設 20 1 2( ) ( ) ( )u A A F A F? ? ?? ? ?, (211) 其中 0 1 2,A A A 為待定常數，且 2 0A? ， ()F? 滿足 廣義 Riccati方程 (25). 利用 (211) 式 與 (25)式可將 (210)的左邊化為關于 ()F? 的多項式 .令 ()F? 的各次冪的系數為 零，得到關于 0 1 2,A A A , ba, , 024,h h h 的代數方程組： ,020xx0: 422224246 ?? hAahAaF ?? ,02424: 421224145 ?? hAAahAaF ?? ,01 2 0612616: 42244224202421222224 ????? hhAahAbhAAahAahAaF ???? ,0418220: 4102221241242143 ???? hAAahAAahAbhhAaF ??? ,0724481612: 042422122222202222402222 ?????? hhAahAahAbhAAahAahAaF ?????,012212: 02122102041422142121 ????? hhAahAAahhAahAahAbF ???? ,02482: 0220202022402120 ???? hAbhAAahhAahAaF ??? 解上述代數方程組得到： .6,0,12 )4( 2 42144 22420 A haAha bhaAA ???? ????? (212)把 (212)式 代 入 (211)式可得：4 2 4 22444444( 4 ) 12 ( )( ) , , ( 0 , 0) 。b b x t?? ? ? ? ? ? ? ?圖 (c)緊孤 波解 ,5,1,4:)( 23 ???? baAu ? 2h ? ,6,7 4?h 。 圖 (g)周期 爆破 波解 ,1,5,8:)( 14226 ??????? ?? khhAu 2k ,2,3 0 ??