Green's Function Method for Periodic Traveling Wave Solutions of the KdV Equation

1983 ◽  
Vol 14 (4) ◽  
pp. 293-301 ◽  
Author(s):  
Liu Bao-Ping ◽  
C. V. Pao ◽  
Ivar Stakgold
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Traveling Wave ◽  
Function Method ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Green’S Function Method ◽  
Wave Solutions ◽  
The Kdv Equation ◽  
Periodic Traveling Wave

scholarly journals Existence Analysis of Traveling Wave Solutions for a Generalization of KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yao Long ◽  
Can Chen
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
System A ◽  
Wave Solutions ◽  
The Kdv Equation

By using the bifurcation theory of dynamic system, a generalization of KdV equation was studied. According to the analysis of the phase portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave, and compactons were discussed. In some parametric conditions, exact traveling wave solutions of this generalization of the KdV equation, which are different from those exact solutions in existing references, were given.

EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED HIROTA–SATSUMA COUPLED KdV EQUATION

2010 ◽  
Vol 24 (22) ◽  
pp. 4333-4355 ◽  
Author(s):  
ZHU LI
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Function Method ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Jacobi Elliptic Function ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Coupled Kdv Equation ◽  
Jacobi Elliptic Function Method

Exact traveling wave solutions of the generalized Hirota–Satsuma coupled KdV equation are obtained by the generalized Jacobi elliptic function method.

scholarly journals Symbolic Computation and the Extended Hyperbolic Function Method for Constructing Exact Traveling Solutions of Nonlinear PDEs

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Huang Yong ◽  
Shang Yadong ◽  
Yuan Wenjun
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Wave Solutions ◽  
Hyperbolic Function Method ◽  
Periodic Traveling Wave

On the basis of the computer symbolic system Maple and the extended hyperbolic function method, we develop a more mathematically rigorous and systematic procedure for constructing exact solitary wave solutions and exact periodic traveling wave solutions in triangle form of various nonlinear partial differential equations that are with physical backgrounds. Compared with the existing methods, the proposed method gives new and more general solutions. More importantly, the method provides a straightforward and effective algorithm to obtain abundant explicit and exact particular solutions for large nonlinear mathematical physics equations. We apply the presented method to two variant Boussinesq equations and give a series of exact explicit traveling wave solutions that have some more general forms. So consequently, the efficiency and the generality of the proposed method are demonstrated.

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method
Sign in / Sign up

Export Citation Format

Share Document