Jacobi elliptic function solutions of nonlinear wave equations via the new sinh-Gordon equation expansion method

2003 ◽  
Vol 36 (7) ◽  
pp. 1961-1972 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Nonlinear Wave ◽  
Elliptic Function ◽  
Wave Equations ◽  
Gordon Equation ◽  
Expansion Method ◽  
Nonlinear Wave Equations ◽  
Jacobi Elliptic Function

scholarly journals Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shi Jing ◽  
Yan Xin-li
Keyword(s):  
Fixed Point ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Expansion Method ◽  
Mapping Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Nonlinear Wave Equations ◽  
Jacobi Elliptic Function ◽  
Long Wave

The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method) can be used to solve other similar nonlinear wave equations.

Separation Transformation and New Exact Solutions for the (1+N)-Dimensional Triple Sine-Gordon Equation

2011 ◽  
Vol 66 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Yifang Liu ◽  
Jiuping Chen ◽  
Weifeng Hu ◽  
Li-Li Zhu
Keyword(s):  
Exact Solution ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Gordon Equation ◽  
Transformation Method ◽  
Nonlinear Wave Equations ◽  
High Dimensional ◽  
Sine Gordon Equation ◽  
New Exact Solutions ◽  
Localized Structures

The separation transformation method is extended to the (1+N)-dimensional triple Sine-Gordon equation and a special type of implicitly exact solution for this equation is obtained. The exact solution contains an arbitrary function which may lead to abundant localized structures of the high dimensional nonlinear wave equations. The separation transformation method in this paper can also be applied to other kinds of high-dimensional nonlinear wave equations

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