(2+1)维Ito方程的孤子解和有理解
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摘要
基于Hirota双线性方法,得到(2+1)维Ito方程的双线性形式,由此可以求得(2+1)维Ito方程的N-孤子解.在二孤子解的基础上,对参数取共轭,可以得到一阶的呼吸子解;再对二孤子解用长波极限和参数限制,则可以得到Ito方程的一阶有理解.
By employing the Hirota bilinear method, the bilinear form of the(2+1)-dimensional Ito equation can be derived. Based on the bilinear form, N-soliton solutions are constructed. On the condition of parameter conjugations, we can obtain breather solutions to the(2+1)-dimensional Ito equation from the two-soliton solution. By taking a long wave limit and making further parameter constraints, one-order rational solution to the(2+1)-dimensional Ito equation can be derived.
By employing the Hirota bilinear method, the bilinear form of the(2+1)-dimensional Ito equation can be derived. Based on the bilinear form, N-soliton solutions are constructed. On the condition of parameter conjugations, we can obtain breather solutions to the(2+1)-dimensional Ito equation from the two-soliton solution. By taking a long wave limit and making further parameter constraints, one-order rational solution to the(2+1)-dimensional Ito equation can be derived.
引文
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[10]Ablowitz M J.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].Cambridge:Cambridge University Press,1992:70-152.
[11]Dickey L A.Solitons Equations and Hamiltonian Systems[M].Singapore:World Scientific,1991:7-20.
[12]Vladimirov A,Maczka C.Exact solutions of generalized burgers equation,describing travelling fronts and their interaction[J].Reports on Mathematical Physics,2007,60(2):317-328.
[13]Bluman G W,Kumei S.Symmetries and differential equations[EB/OL].[2018-10-10].https://link.springer.com/book/10.1007%2F978-1-4757-4307-4.
[14]Ohta Y,Wang D S,Yang J.General N-dark-dark solitons in the coupled nonlinear Schr?dinger equations[J].Studies in Applied Mathematics,2011,17(4):345-371.
[15]Rao J G,Cheng Y,He J S.Rational and semi-rational solution of the nonlocal Davey-Stewardton[J].Studies in Applied Mathematics,2017,139:568-598.
[16]Wang X B,Tian S F,Qin C Y,et al.Dynamics of the breathers,rogue waves and solitary waves in the(2+1)-dimensional Ito equation[J].Applied Mathematics Letters,2018,68:40-47.
[17]Yang J Y,Ma W X,Qin Z Y.Lump and lump-soliton solutions to the(2+1)-dimensional Ito equation[J].Analysis and Mathematical Physics,2018,8:427-436.
[18]Zhang Y,Chen D Y.N-soliton-like solution of Ito equation[J].Communications in Theoretical Physics,2004,42:641-644.
[2]Wang L,Li M,Qi F H,et al.Modulational instability,nonautonomous breathers and rouge waves for a variable-coefficient derivative nonlinear Schr?dinger equation in the inhomogeneous[J].Plasmas,2015,22:1-10.
[3]Mihalache D.Multidimensional localized structures in optical and Bose-Einstein condensates:A selection of recent studies[J].Romanian Journal of Physics,2014,59:295-312.
[4]Malomed B,Torner L,Wise F,et al.On multidimensional solitons and their legacy in contemporary atomic,molecular and optical physics[J].Journal of Physics B-Atomic Molecular and Optical Physics,2016,49(17):1-32.
[5]Bagnato V S,Frantzeskakis D J,Kevrekidis P G,et al.Bose-Einstein condensation:Twenty year after[J].Romanian Journal of Physics,2015,67:251-253.
[6]Matveev V B,Salle M A.Darboux transformation and solitons[EB/OL].[2018-10-10].https://zbmath.org/0744.35045.
[7]谷超豪,胡和生,周子翔.孤子理论中的达布变换及其几何应用[M].上海:上海科学技术出版社,1999:1-47.
[8]Matsuno Y.Bilinear transformation method[EB/OL].[2018-10-10].https://zbmath.org/0552.35001.
[9]Hirota R.The Direct Method in Soliton Theory[M].Cambridge:Cambridge University Press,2004:1-58.
[10]Ablowitz M J.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].Cambridge:Cambridge University Press,1992:70-152.
[11]Dickey L A.Solitons Equations and Hamiltonian Systems[M].Singapore:World Scientific,1991:7-20.
[12]Vladimirov A,Maczka C.Exact solutions of generalized burgers equation,describing travelling fronts and their interaction[J].Reports on Mathematical Physics,2007,60(2):317-328.
[13]Bluman G W,Kumei S.Symmetries and differential equations[EB/OL].[2018-10-10].https://link.springer.com/book/10.1007%2F978-1-4757-4307-4.
[14]Ohta Y,Wang D S,Yang J.General N-dark-dark solitons in the coupled nonlinear Schr?dinger equations[J].Studies in Applied Mathematics,2011,17(4):345-371.
[15]Rao J G,Cheng Y,He J S.Rational and semi-rational solution of the nonlocal Davey-Stewardton[J].Studies in Applied Mathematics,2017,139:568-598.
[16]Wang X B,Tian S F,Qin C Y,et al.Dynamics of the breathers,rogue waves and solitary waves in the(2+1)-dimensional Ito equation[J].Applied Mathematics Letters,2018,68:40-47.
[17]Yang J Y,Ma W X,Qin Z Y.Lump and lump-soliton solutions to the(2+1)-dimensional Ito equation[J].Analysis and Mathematical Physics,2018,8:427-436.
[18]Zhang Y,Chen D Y.N-soliton-like solution of Ito equation[J].Communications in Theoretical Physics,2004,42:641-644.