scholarly journals Joint Application of Bilinear Operator and F-Expansion Method for (2+1)-Dimensional Kadomtsev-Petviashvili Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shaolin Li ◽  
Yinghui He ◽  
Yao Long
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Expansion Method ◽  
Traveling Wave Solution ◽  
Bilinear Operator ◽  
Test Function ◽  
Joint Application ◽  
Petviashvili Equation

The bilinear operator and F-expansion method are applied jointly to study (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation. An exact cusped solitary wave solution is obtained by using the extended single-soliton test function and its mechanical feature which blows up periodically in finite time for cusped solitary wave is investigated. By constructing the extended double-soliton test function, a new type of exact traveling wave solution describing the assimilation of solitary wave and periodic traveling wave is also presented. Our results validate the effectiveness for joint application of the bilinear operator and F-expansion method.

scholarly journals General Traveling Wave Solutions of Nonlinear Conformable Fractional Sharma-Tasso-Olever Equations and Discussing the Effects of the Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kai Fan ◽  
Rui Wang ◽  
Cunlong Zhou
Keyword(s):  
General Solution ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Wave Solution ◽  
Fractional Derivatives ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Traveling Wave Solution ◽  
Complex Transformation ◽  
Further Development

The exact traveling wave solution of the fractional Sharma-Tasso-Olever equation can be obtained by using the function expansion method, but the general traveling wave solution cannot be obtained. After transforming it into the Sharma-Tasso-Olever equation of the integer order by the fractional complex transformation, the general solution of its traveling wave is obtained by a specific function transformation. Through parameter setting, the solution of the kinked solitary wave is found from the general solution of the traveling wave, and it is found that when the two fractional derivatives become smaller synchronically, the waveform becomes more smooth, but the position is basically unchanged. The reason for this phenomenon is that the kink solitary wave reaches equilibrium in the counterclockwise and clockwise rotation, and the stretching phenomenon is accompanied in the process of reaching equilibrium. This is a further development of our previous work, and this kind of detailed causative analysis is rare in previous papers.

Traveling Wave Solution of (2+1) Dimensional Breaking Soliton Equation by Bernoulli Sub-ODE Method

2011 ◽  
Vol 403-408 ◽  
pp. 207-211
Author(s):  
Qing Hua Feng ◽  
Yu Lu Wang
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
Traveling Wave ◽  
Wave Solution ◽  
Present Method ◽  
Expansion Method ◽  
Traveling Wave Solution ◽  
Soliton Equation ◽  
Ode Method

In this paper, we derive exact traveling wave soluti-ons of (2+1) dimensional breaking soliton equation by a proposed Bernoulli sub-ODE method. The method appears to be efficient in seeking exact solutions of nonlinear equations. We also make a comparison between the present method and the known (G’/G) expansion method.

Study of the Solitoff Solution and Fractal Solution for the (2+1)-Dimensional Broek-Kaup System with Variable Coefficients

2014 ◽  
Vol 532 ◽  
pp. 356-361
Author(s):  
Wei Ting Zhu
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Expansion Method ◽  
Variable Coefficients ◽  
Variable Separation ◽  
New Family ◽  
Localized Excitations ◽  
Variable Separation Method

Starting from a (G'/G)-expansion method and a variable separation method, a new family of exact solutions of the (2+1)-dimensional Broek-Kaup system with variable coefficients(VCBK) is obtained. Based on the derived solitary wave solution, we obtain some special localized excitations such as solitoff solutions and fractal solutions.

scholarly journals Expanded (G/G2) Expansion Method to Solve Separated Variables for the 2+1-Dimensional NNV Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Yong Meng
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Fractal Structure ◽  
Expansion Method ◽  
Generalized Solution ◽  
Traveling Wave Solution ◽  
Extended Form ◽  
Positive Power ◽  
Negative Power ◽  
Separated Variables

The traditional (G/G2) expansion method is modified to extend the symmetric extension to the negative power term in the solution to the positive power term. The general traveling wave solution is extended to a generalized solution that can separate variables. By using this method, the solution to the detached variables of the symmetric extended form of the 2+1-dimensional NNV equation can be solved, also the soliton structure and fractal structure of Dromion can be studied well.

scholarly journals Exact Solitary Wave Solution in the ZK-BBM Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Juan Zhao ◽  
Wei Li
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Homoclinic Orbits ◽  
Traveling Wave Solution ◽  
Phase Portraits ◽  
Dynamical System Theory ◽  
Ode System ◽  
Nonlinear Ode ◽  
Bbm Equation

The traveling wave solution for the ZK-BBM equation is considered, which is governed by a nonlinear ODE system. The bifurcation structure of fixed points and bifurcation phase portraits with respect to the wave speed c are analyzed by using the dynamical system theory. Furthermore, the exact solutions of the homoclinic orbits for the nonlinear ODE system are obtained which corresponds to the solitary wave solution curve of the ZK-BBM equation.

Traveling Wave Solution of (3+1) Dimensional Potential-YTSF Equation by Bernoulli Sub-ODE Method

2011 ◽  
Vol 403-408 ◽  
pp. 212-216
Author(s):  
Qing Hua Feng
Keyword(s):  
Exact Solutions ◽  
Nonlinear Equations ◽  
Traveling Wave ◽  
Wave Solution ◽  
Present Method ◽  
Expansion Method ◽  
Traveling Wave Solution ◽  
Ode Method ◽  
Ytsf Equation ◽  
Potential Ytsf Equation

In this paper, we derive exact traveling wave soluti-ons of (3+1) dimensional potential-YTSF equation by a proposed Bernoulli sub-ODE method. The method appears to be efficient in seeking exact solutions of nonlinear equations. We also make a comparison between the present method and the known (G’/G) expansion method.

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