Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations

2005 ◽  
Vol 343 (1-3) ◽  
pp. 48-54 ◽  
Author(s):  
Mingliang Wang ◽  
Xiangzheng Li
Keyword(s):  
Expansion Method ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions

Nonlocal Symmetry and Consistent Tanh Expansion Method for the Coupled Integrable Dispersionless Equation

2016 ◽  
Vol 71 (3) ◽  
pp. 235-240 ◽  
Author(s):  
Hengchun Hu ◽  
Xiao Hu ◽  
Bao-Feng Feng
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Cnoidal Wave ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Periodic Wave Solutions ◽  
Wave Solutions

AbstractNonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

M-fractional solitons and periodic wave solutions to the Hirota–Maccari system

2019 ◽  
Vol 33 (05) ◽  
pp. 1950052 ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Gulnur Yel ◽  
Hasan Bulut
Keyword(s):  
Fractional Derivative ◽  
Gordon Equation ◽  
Expansion Method ◽  
Periodic Wave ◽  
3 Dimensional ◽  
Periodic Wave Solutions ◽  
Wave Solutions

In this study, we construct several wave solutions to the nonlinear fractional Hirota–Maccari equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. The constraint conditions that guarantee the existence of valid solutions are stated. We use suitable values of parameters in plotting the 2- and 3-dimensional graphs of the reported solutions.

Investigation of (G'/G)-Expansion Method and Exact Solutions for the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff System

2013 ◽  
Vol 432 ◽  
pp. 235-239
Author(s):  
Gen Hai Xu ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Family ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and the (G'/G)-expansion method and a linear variable separation method, a new family of exact solutions (including solitary wave solutions,periodic wave solutions and rational function solutions) of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff system (2DCBS) is derived.

Breather-wave, periodic-wave and traveling-wave solutions for a (2 + 1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation for an incompressible fluid

2021 ◽  
pp. 2150261
Author(s):  
Yuan Shen ◽  
Bo Tian ◽  
Chen-Rong Zhang ◽  
He-Yuan Tian ◽  
Shao-Hua Liu
Keyword(s):  
Incompressible Fluid ◽  
Theta Function ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Polynomial Expansion Method

In this paper, the investigation is conducted on a (2 + 1)-dimensional extended Boiti–Leon–Manna–Pempinelli equation for an incompressible fluid. Via the Riemann theta function, periodic-wave solutions are derived, and breather-wave solutions are constructed with the aid of the extended homoclinic test approach. Based on the polynomial expansion method, several traveling-wave solutions are derived. Besides, we observe that the amplitude of the breather keeps unchanged during the propagation and the traveling wave which is kink shaped propagates stably. Furthermore, we analyze the transition between the periodic-wave and soliton solutions, which implies that the periodic-wave solutions tend to the soliton solutions via a limiting procedure.

scholarly journals Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Weimin Zhang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Function Expansion ◽  
Jacobi Elliptic Function Expansion

The extended Jacobi elliptic function expansion method is applied for Zakharov-Kuznetsov-modified equal-width (ZK-MEW) equation. With the aid of symbolic computation, we construct some new Jacobi elliptic doubly periodic wave solutions and the corresponding solitary wave solutions and triangular functional (singly periodic) solutions.

scholarly journals The (G′/G,1/G)-Expansion Method and Its Applications to Find the Exact Solutions of Nonlinear PDEs for Nanobiosciences

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
E. M. E. Zayed ◽  
K. A. E. Alurrfi
Keyword(s):  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Periodic Wave ◽  
Nonlinear Pdes ◽  
Mathematical Tool ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Powerful Mathematical Tool

The two-variable (G′/G,1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of nanobiosciences partial differential equation. When the parameters are replaced by special values, the solitary wave solutions and the periodic wave solutions of this equation have been obtained from the traveling waves. This method can be thought of as the generalization of well-known originalG′/G-expansion method proposed by M. Wang et al. It is shown that the two-variable (G′/G,1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics. Comparison between our results and the well-known results is given.

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