常系数耦合mKdV方程的复合型新解
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摘要
利用一种函数变换与第一种椭圆方程相结合的方法,构造了常系数耦合mKdV方程的由Riemann θ函数、Jacobi椭圆函数、双曲函数和三角函数两两组合的双孤子解、双周期解以及孤子解与周期解组合的无穷序列复合型新解.
The method for combining a kind of a function transformation and the first kind of elliptic equation is presented to construct the new infinite sequence complexion solutions to couple mKdV equation of constant coefficients, which are composed of two-soliton solutions,two-period solutions, soliton solutions and period solutions in any two functions of Riemann θ function, Jacobi elliptic function, hyperbolic function and trigonometric function.
The method for combining a kind of a function transformation and the first kind of elliptic equation is presented to construct the new infinite sequence complexion solutions to couple mKdV equation of constant coefficients, which are composed of two-soliton solutions,two-period solutions, soliton solutions and period solutions in any two functions of Riemann θ function, Jacobi elliptic function, hyperbolic function and trigonometric function.
引文
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[12] Md Nur Alam,Md Ali Akbar,Syed Tauseef Mohyud Din.A novel(G'(ξ)/G(ξ))-expansion method and its application to the Boussinesq equation[J]. Chinese Physics B, 2014, 23(2):020203(1-10).
[13]套格图桑.辅助方程构造CH-r方程的无穷序列尖峰孤立波解[J].工程数学学报,2012, 29(6):865-876.
[14] Xie F D, Chen J, Lii Z S. Using symbolic computation to exactly solve the integrable Broer-Kaup equations in(2+1)-dimensional spaces[J]. Communnications in Theoretical Physics, 2005, 43(4):585-590.
[15]马正义,马松华,杨毅.具有色散系数的(2+1)维非线性Schrodinger方程的有理解和空间孤子[J].物理学报,2012, 61(19):190508(1-5).
[16]套格图桑,伊丽娜. Sine-Gordon型方程的无穷序列新解[J].物理学报,2014,63(21):215202(1-9).
[17] Taogetusang, Sirendaoerji, Li Shu Min. New application to riccati equation[J]. Chinese Physics B,2010, 19(8):080303(1-8).
[18] Taogetusang, Sirendaoerji, Li Shu Min. Infinite sequence soliton-like exact solutions of the(2+1)-dimensional breaking soliton equation[J]. Communnications in Theoretical Physics, 2011, 47(6):949-954.
[19]王军民.修正的Korteweg de Vries-正弦Gordon方程的Riemannθ函数解[J].物理学报,2012, 61(8):080201(1-5).
[2] Fu Z T, Liu S K, Liu S D. A new approach to solve nonlinear wave equations[J]. Communnications in Theoretical Physics(Beijing, China), 2003, 39(1):27-30.
[3] Fu Z T, Liu S K, Liu S D. New Rational form solutions to mKdV equation[J]. Communnications in Theoretical Physics(Beijing, China), 2005, 43(3):423-426.
[4] Yang J R, Mao J J. Complexiton solutions of a special coupled mKdV system[J]. Chinese Physics Lett, 2008, 25(5):1527-1530.
[5] E.F. El-Shamy. Dust-ion-acoustic solitary waves in a hot magnetized dusty plasma with charge fluctuations[J]. Chaos,Solitons and Fractals, 2005, 25:665-674.
[6] Smyth N F, Worhty A L. Solitary wave evolution for mKdV equations[J]. Wave Motion, 1995, 21:263-275.
[7]罗德海.大气中大尺度包络孤立子理论与阻塞环流[M].北京:气象出版社,1999.
[8] Lee S, Masui T, Yamamoto A, et al. Superconductivity and its applications[J]. Physica C, 2003,397:7-13.
[9]余丽琴,田立新. Degasperis-Procesi方程的孤立尖波解[J].数学的实践与认识,2006,36(3):261-266.
[10] Chen Y, Li B, Zhang H Q. Generalized Riccati equation expansion method and its application to the Bogoyavlenskiis generalized breaking soliton equation[J]. Chinese Physics, 2003, 12(9):940-945.
[11] Khaled A. Gepreel, Saleh Omran.exact solutions for nonlinear partial fractional differential equations[J]. Chinese Physics B, 2012, 21(11):110204(1-7).
[12] Md Nur Alam,Md Ali Akbar,Syed Tauseef Mohyud Din.A novel(G'(ξ)/G(ξ))-expansion method and its application to the Boussinesq equation[J]. Chinese Physics B, 2014, 23(2):020203(1-10).
[13]套格图桑.辅助方程构造CH-r方程的无穷序列尖峰孤立波解[J].工程数学学报,2012, 29(6):865-876.
[14] Xie F D, Chen J, Lii Z S. Using symbolic computation to exactly solve the integrable Broer-Kaup equations in(2+1)-dimensional spaces[J]. Communnications in Theoretical Physics, 2005, 43(4):585-590.
[15]马正义,马松华,杨毅.具有色散系数的(2+1)维非线性Schrodinger方程的有理解和空间孤子[J].物理学报,2012, 61(19):190508(1-5).
[16]套格图桑,伊丽娜. Sine-Gordon型方程的无穷序列新解[J].物理学报,2014,63(21):215202(1-9).
[17] Taogetusang, Sirendaoerji, Li Shu Min. New application to riccati equation[J]. Chinese Physics B,2010, 19(8):080303(1-8).
[18] Taogetusang, Sirendaoerji, Li Shu Min. Infinite sequence soliton-like exact solutions of the(2+1)-dimensional breaking soliton equation[J]. Communnications in Theoretical Physics, 2011, 47(6):949-954.
[19]王军民.修正的Korteweg de Vries-正弦Gordon方程的Riemannθ函数解[J].物理学报,2012, 61(8):080201(1-5).