The first integral and new infinite sequence solutions of (n+1)-dimensional multiple sine-Gordon equation

Abstract

Abstract: The solution of (n+1)-dimensional multiple sine-Gordon equation is transformed into solution of the set of ordinary differential equations by several function transformations. New infinite sequence soliton-like solutions of (n+1)-dimensional multiple sine-Gordon equation are constructed by combining the first integrals of the set of ordinary differential equations with B?cklund transformation and the nonlinear superposition formula of solutions to several kinds of solvable ordinary differential equations.

Key words: the first integral; (n+1)-dimensional multiple sine-Gordon equation; B?cklund transformation; new infinite sequence soliton-like solutions

CLC Number:

O175.29

References

[1]Li Jibin.Exact travelling wave solutions and dynamical behavior for the (n+1)-dimensional multiple sine-Gordon equation[J].Science.China.Series A:Mathematics, 2007,50(2):153-164.
[2]Taogetusang,Sirendaoerji.New exact solutions to (n+1)-dimensional double sine-Gordon equation[J].Acta.Phys. Sin.(物理学报), 2010,59(8):5194-5201(in Chinese).
[3]Li Jibin,Li M.Bounded travelling wave solutions for the (n+1)-dimensional sine-Gordon equation[J].Chaos. Solitons and Fractals,2005, 25:1037-1047.
[4]A M Wazwaz.The tanh method and a variable separated ODE method for solving double sine-Gordon equation[J].Phys.Lett.A,2006, 350:367-370.
[5]Taogetusang,Bai Yymei.Riemann theta function and other several kinds of new solutions of nonlinear evolution equations[J].Acta.Phys.Sin.(物理学报),2013, 62(10):100201(in Chinese).
[6]Taogetusang,Sirendaoerji,Li Shumin.Infinite sequence soliton-like exact solutions fo (2+1)-dimensional Breaking soliton equation[J]. Commun.Theor.Phys.(Beijing),2011,55(6): 949-954.
[7]Taogetusang, Sirendaoerji.Jacobi elliptic function exact solutions of sine-Gordon equation[J].Chinese Journal of quantum electronics(量子电子学报),2009,26(3):278-287(in Chinese).
[8]Wang Junmin.Riemann \theta function solutions to modified Korteweg de Vries-sine-Gordon equation[J]. Acta.Phys.Sin.(物理学报),2012,61(8): 080201(1-5)(in Chinese).
[9]Ma Zhengyi, Ma Songhua, Yang Yi.Rational solutions and spatial solitons for the (2+1)-dimensional nonlinear schr\"{o}dinger equation with distributed coefficents[J].Acta.Phys.Sin.(物理学报), 2012,61 190508(1-5)(in Chinese)
[10]Liu Chengshi.Travelling wave solutions of triple sine-Gordon equation[J]. Chin.Phys.Lett,2004, 21(12):2369-2371.
[11]Ma Songhua, Fang Jianping. Peaked soliton solutions and interaction between solitons for the extended (2+1)-dimensional shallow water wave equation[J]. Acta.Phys.Sin.(物理学报),2012,61 180505(1-6)(in Chinese)
[12]Chen Yong, Li Biao. New exact travelling wave solutions for Generalized Zakharov-Kuzentsov equations using general Projective Riccati equation method[J]. Commun.Theor.Phys.(Beijing),2004,41:1-6
[13]Khaled A. Gepreel, Saleh Omran.Exact solutions for nonlinear partial fractional differential equations[J]. Chin. Phys.B,2012, 21(11):110204.
[14]Md Nur Alam,Md Ali Akbar,Syed Tauseef Mohyud Din.A novel (G’/G)-expansion method and its application to the Boussinesq equation[J].
Chin.Phys.B,2014,23(2): 020203.