Solitons, Backlund transformations, Lax pair and conservation laws for the nonautonomous mKdV-sinh-Gordon equation with time-dependent coefficients

被引：3
作者：
Liu, Lei
Tian, Bo [1 ]
Sun, Wen-Rong
Wang, Yu-Feng
Wang, Yun-Po
机构：
[1] Beijing Univ Posts & Telecommun, State Key Lab Informat Photon & Opt Commun, Beijing 100876, Peoples R China
来源：
MODERN PHYSICS LETTERS B | 2016年 / 30卷 / 03期
基金：
中国国家自然科学基金;
关键词：
mKdV-sinh-Gordon equation with time-dependent coefficients; binary Bell polynomials; Hirota method; Backlund transformations; Lax pair; conservation laws; symbolic computation; FERROMAGNETIC SPIN CHAIN; DE-VRIES EQUATION; SOLITARY WAVES; KORTEWEG; MODEL; PLASMA;
D O I：
10.1142/S0217984916500081
中图分类号：
O59 [应用物理学];
学科分类号：
摘要：
The transition phenomenon of few-cycle-pulse optical solitons from a pure modified Korteweg-de Vries (mKdV) to a pure sine-Gordon regime can be described by the non-autonomous mKdV-sinh-Gordon equation with time-dependent coefficients. Based on the Bell polynomials, Hirota method and symbolic computation, bilinear forms and soliton solutions for this equation are obtained. Backlund transformations (BTs) in both the binary Bell polynomial and bilinear forms are obtained. By virtue of the BTs and Ablowitz-Kaup-Newell-Segur system, Lax pair and infinitely many conservation laws for this equation are derived as well.
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页数：12
相关论文
共 46 条
[1]  
Ablowitz M., 1991, Soliton, Nonlinear Evolution Equations and Inverse Scattering
[2]   NONLINEAR-EVOLUTION EQUATIONS OF PHYSICAL SIGNIFICANCE [J].
ABLOWITZ, MJ ;
KAUP, DJ ;
NEWELL, AC ;
SEGUR, H .
PHYSICAL REVIEW LETTERS, 1973, 31 (02) :125-127
[3]  
[Anonymous], 1980, DIRECT METHOD SOLITO
[4]   Exponential polynomials [J].
Bell, ET .
ANNALS OF MATHEMATICS, 1934, 35 :258-277
[5]   Response to "Comment on 'A new mathematical approach for finding the solitary waves in dusty plasma'" [Phys. Plasmas 6, 4392 (1999)] [J].
Das, GC ;
Sarma, J .
PHYSICS OF PLASMAS, 1999, 6 (11) :4394-4397
[6]   Anti-dark solitons for a variable-coefficient higher-order nonlinear Schrodinger equation in an inhomogeneous optical fiber [J].
Feng, Yu-Jie ;
Gao, Yi-Tian ;
Sun, Zhi-Yuan ;
Zuo, Da-Wei ;
Shen, Yu-Jia ;
Sun, Yu-Hao ;
Xue, Long ;
Yu, Xin .
PHYSICA SCRIPTA, 2015, 90 (04)
[7]   Cylindrical Kadomtsev-Petviashvili model, nebulons and symbolic computation for cosmic dust ion-acoustic waves [J].
Gao, YT ;
Tian, B .
PHYSICS LETTERS A, 2006, 349 (05) :314-319
[8]   METHOD FOR SOLVING KORTEWEG-DEVRIES EQUATION [J].
GARDNER, CS ;
GREENE, JM ;
KRUSKAL, MD ;
MIURA, RM .
PHYSICAL REVIEW LETTERS, 1967, 19 (19) :1095-&
[9]   Nonautonomous mixed mKdV-sinh-Gordon hierarchy [J].
Gomes, J. F. ;
de Melo, G. R. ;
Ymai, L. H. ;
Zimerman, A. H. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (39)
[10]   A class of mixed integrable models [J].
Gomes, J. F. ;
de Melo, G. R. ;
Zimerman, A. H. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (27)
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