New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation

Taogetusang

doi:10.21656/1000-0887.370211

Volume 38 Issue 5

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Taogetusang. New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2017, 38(5): 553-560. doi: 10.21656/1000-0887.370211

Citation:

Taogetusang. New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2017, 38(5): 553-560. doi: 10.21656/1000-0887.370211

Citation:

Taogetusang. New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2017, 38(5): 553-560. doi: 10.21656/1000-0887.370211

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New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation

doi: 10.21656/1000-0887.370211

Taogetusang

Mathematics Science College, Inner Mongolia Normal University, Huhhot 010022, P.R.China

Funds: The National Natural Science Foundation of China(11361040)

Received Date: 2016-07-01
Rev Recd Date: 2016-08-24
Publish Date: 2017-05-15

Abstract

Abstract

The method combining the auxiliary equation, the function transformation and the variable separation solutions was proposed to construct the new 2-soliton and 2-period solutions to the arbitrary order nonlinear Camassa-Holm equation. Step 1, with 2 auxiliary equations, the function transformation and the variable separation solutions, the problem of solving the arbitrary order nonlinear Camassa-Holm equation was transformed to the problem of solving the nonlinear algebraic equations. Step 2, by means of symbolic computation system Mathematica, the solutions to the algebraic equations were obtained, and with the help of the relative conclusions on the auxiliary equation, the new 2-soliton and 2-period solutions were constructed.
- function transformation,
- variable separation solution,
- arbitrary order nonlinear Camassa-Holm equation,
- new 2-soliton solution

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References(10)

References

[1]	Camassa R, Holm D D. An integrable shallow water equation with peaked solitons[J]. Phys Rev Lett,1993,71(13): 1661-1664.
[2]	殷久利, 田立新. 一类非线性方程的compacton解及其移动compacton 解[J]. 物理学报, 2004,53(9): 2821-2827.(YIN Jiu-li, TIAN Li-xin. Compacton solutions and floating compacton solutions of one type of nonlinear equations[J]. Acta Physica Sinica,2004,53(9): 2821-2827.(in Chinese))
[3]	CHEN Yong, LI Biao. New exact travelling wave solutions for generalized Zakharov-Kuznetsov equations using general projective Riccati equation method[J]. Commun Theor Phys,2004,41(1): 1-6.
[4]	Sirendaoerji, SUN Jong. Adirect method for solving sine-Gordon type equations[J]. Phys Lett A ,2002,298(3):133-139.
[5]	Gepreel K A, Omran S. Exact solutions for nonlinear partial fractional differential equations[J]. Chinese Physics B,2012,21(11): 110204.
[6]	Alam M N, Akbar M A, Mohyud-Din S T. A novel (G′/G) -expansion method and its application to the Boussinesq equation[J]. Chinese Physics B,2014,23(2): 020203.
[7]	马松华, 方建平. 扩展的(2+1)维浅水波方程的尖峰孤子解及其相互作用[J]. 物理学报, 2012,61(18): 180505-1-180505-6.(MA Song-hua, FANG Jian-ping. Peaked soliton solutions and interaction between solitons for the extended (2+1)-dimensional shallow water wave equation[J]. Acta Physica Sinica,2012,61(18): 180505-1-180505-6.(in Chinese))
[8]	套格图桑, 白玉梅. 非线性发展方程的Riemann theta 函数等几种新解[J]. 物理学报, 2013,62(10): 100201-1-100201-9.(Taogetusang, BAI Yu-mei. Riemann theta function and other several kinds of new solutions of nonlinear evolution equations[J]. Acta Physica Sinica,2013,62(10): 100201-1-100201-9.(in Chinese))
[9]	杨小锋, 邓子辰, 魏乙. 基于Riccati-Bernoulli辅助常微分方程的Davey-Stewartson方程的行波解[J]. 应用数学和力学, 2015,36(10): 1067-1075.(YANG Xiao-feng, DENG Zi-chen, WEI Yi. Traveling wave solutions to the Davey-Stewartson equation with the Riccati-Bernoulli sub-ODE method[J]. Applied Mathematics and Mechanics,2015,36(10): 1067-1075.(in Chinese))
[10]	那仁满都拉, 额尔敦仓. 立方非线性微结构固体中的对称孤立波及存在条件[J]. 应用数学和力学,2014,35(11):1210-1217.(Narenmandula, Eerduncang. Symmetric solitary waves and their existence conditions in cubic nonlinear microstructured solids[J]. Applied Mathematics and Mechanics,2014,35(11): 1210-1217.(in Chinese))