利用修正的Clarkson-Kruskal (CK)直接方法得到了含色散项的Zabolotskaya-Khokhlov(简写为DZK)方程的对称、约化和一些精确解,包括双曲函数解,有理函数解,三角函数解等,同时得到了该方程的守恒律.
参考文献
[1] | Zhongzhou DONG;Yong CHEN;Dexing KONG;Zenggui WANG.Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Ampère Equation[J].数学年刊B辑(英文版),2012(02):309-316. |
[2] | HU Xiao-Rui;CHEN Yong;QIAN Long-Jiang.Full Symmetry Groups and Similar Reductions of a (2+1)-Dimensional Resonant Davey-Stewartson System[J].理论物理通讯(英文版),2011(5):737-742. |
[3] | Chen J C;Xin X P;Chen Y.Nonlocal symmetries of the Hirota-Satsuma coupled Korteweg-de Vries and their applications exact interaction solutions and integrable hierarchy system[J].Journal of Mathematical Physics,201455:053508. |
[4] | Rogers C;Schief W K.Backlund and Darboux Transformations,Geometry and Morden Applications in Soliton Theory[M].Cambridge:Cambridge University Press,2002 |
[5] | Hirota R.The Direct Method in Soliton Theory[M].Cambridge:Cambridge University Press,2004 |
[6] | Wang M L;Zhou Y B;Li Z B.Application of a homogeneous banlance method to exact solutions of nonlinear equations in mathematical physics[J].Physics Letters A,1996216(1):67-75. |
[7] | Liu XQ.;Jiang S..The sec(q)-tanh(q)-method and its applications[J].Physics Letters, A,20024(4):253-258. |
[8] | 陈美;刘希强.Konopelchenko-Dubrovsky方程组的对称,精确解和守恒律[J].纯粹数学与应用数学,2011(4):533-539,568. |
[9] | Xin X P;Liu X Q;Zhang L L.Symmetry reduction,exact solutions and conservation laws of the modified Kadomtzev-Patvishvili-Ⅱ equation[J].Physics Letters,201128(2):020201-1-020201-4. |
[10] | 张颖元;刘希强;王岗伟.BogoyavlenskiiKadontsevPetviashili方程的新的显式解[J].昆明学院学报,2012(3):55-59. |
[11] | ZHANG Li-Hua;LIU Xi-Qiang.New Exact Solutions and Conservation Laws to (3+1)-Dimensional Potential-YTSF Equation[J].理论物理通讯(英文版),2006(03):487-492. |
[12] | Clarkson P A;Kruskal M D.New similarity solutions of the Boussinesq equation[J].Journal of Mathematical Physics,198930:2201-2213. |
[13] | Li, B.-Q.;Li, S.;Ma, Y.-L..New exact solution and novel time solitons for the dissipative Zabolotskaya-Khokhlov equation from nonlinear acoustics[J].Zeitschrift fur Naturforschung, A. A journal of physical sciences,201210/11(10/11):601-607. |
[14] | Liu X J;Mei C L;Ma S H.Traveling wave solutions and kind wave excitations for the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation[J].Applied Mathematics,20134:1595-1598. |
[15] | Masayoshi T.Similarity reductions of the Zabolotskaya-Khokhlov equation with a dissipative term[J].Nonlinear Mathematical Physics,19952:392-397. |
[16] | Lu D;Hong B.New exact solutions for the (2+1)-dimensional generalized Broer-Kaup system[J].Applied mathematics and computation,20082(2):572-580. |
[17] | Nail H. Ibragimov.A new conservation theorem[J].Journal of Mathematical Analysis and Applications,20071(1):311-328. |
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