scholarly journals EXPANSION METHOD ABOUT THE JACOBI ELLIPTIC FUNCTION ANDITS APPLICATIONS TO NONLINEAR WAVE EQUATIONS

2001 ◽  
Vol 50 (11) ◽  
pp. 2068
Author(s):  
LIU SHI-KUO ◽  
FU ZUN-TAO ◽  
LIU SHI-DA ◽  
ZHAO QIANG
Keyword(s):  
Nonlinear Wave ◽  
Elliptic Function ◽  
Wave Equations ◽  
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.

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