A New Simplified Bilinear Method for the N-Soliton Solutions for a Generalized FmKdV Equation with Time-Dependent Variable Coefficients

被引：37
作者：
Alquran, Marwan [1 ,2 ]
Jaradat, H. M. [3 ]
Al-Shara', Safwan [3 ]
Awawdeh, Fadi [4 ,5 ]
机构：
[1] Jordan Univ Sci & Technol, Dept Math & Stat, Irbid 22110, Jordan
[2] Sultan Qaboos Univ, Dept Math & Stat, Muscat 123, Oman
[3] Al Al Bayt Univ, Dept Math, Al Mafraq 25113, Jordan
[4] Hashemite Univ, Dept Math, Zarqa 13115, Jordan
[5] Dhofar Univ, Dept Math & Sci, Salalah 211, Oman
来源：
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION | 2015年 / 16卷 / 06期
关键词：
Hirota bilinear method; N-soliton solutions; modified Riemann-Liouville derivative; variable coefficients FmKdV equation; FRACTIONAL DIFFERENTIAL-EQUATION; AUTO-BACKLUND TRANSFORMATION; DIFFUSION-WAVE EQUATIONS; DE-VRIES EQUATION; ADOMIAN DECOMPOSITION; MULTIPLE COLLISIONS; ANALYTIC SOLUTIONS; KDV EQUATION; ORDER;
D O I：
10.1515/ijnsns-2014-0023
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper a generalized fractional modified Korteweg-de Vries (FmKdV) equation with time-dependent variable coefficients, which is a generalized model in nonlinear lattice, plasma physics and ocean dynamics, is investigated. With the aid of a simplified bilinear method, fractional transforms and symbolic computation, the corresponding N-soliton solutions are given and illustrated. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Finally, the resonance phenomenon for the equation is examined.
引用
收藏
页码：259 / 269
页数：11
相关论文
共 41 条
[1]  
[Anonymous], 1980, DIRECT METHODS SOLIT
[2]  
[Anonymous], 2002, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Aribitrary Order
[3]   Symbolic Computation on Soliton Solutions for Variable-coefficient Quantum Zakharov-Kuznetsov Equation in Magnetized Dense Plasmas [J].
Awawdeh, Fadi ;
Al-Shara', Safwan ;
Jaradat, H. M. ;
Alomari, A. K. ;
Alshorman, Rafat .
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2014, 15 (01) :35-45
[4]   Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma [J].
Awawdeh, Fadi ;
Jaradat, H. M. ;
Al-Shara, S. .
EUROPEAN PHYSICAL JOURNAL D, 2012, 66 (02)
[5]   Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian decomposition method [J].
Daftardar-Gejji, Varsha ;
Bhalekar, Sachin .
APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (01) :113-120
[6]   Solving a multi-order fractional differential equation using adomian decomposition [J].
Daftardar-Gejji, Varsha ;
Jafari, Hossein .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 189 (01) :541-548
[7]   Application of generalized differential transform method to multi-order fractional differential equations [J].
Erturk, Vedat Suat ;
Momani, Shaher ;
Odibat, Zaid .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2008, 13 (08) :1642-1654
[8]   Fractional calculus - A new approach to the analysis of generalized fourth-order diffusion-wave equations [J].
Golbabai, A. ;
Sayevand, K. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (08) :2227-2231
[9]  
Golbabai A, 2010, Nonlinear Sci Lett A, V1, P147
[10]   On the integrability properties of variable coefficient Korteweg de Vries equations [J].
Gungor, F ;
Sanielevici, M ;
Winternitz, P .
CANADIAN JOURNAL OF PHYSICS, 1996, 74 (9-10) :676-684
12345