A new general algebraic method with symbolic computation to construct new travelling wave solution for the (1+1)-dimensional dispersive long wave equation

2005 ◽  
Vol 168 (2) ◽  
pp. 1189-1204 ◽  
Author(s):  
Yong Chen ◽  
Qi Wang
Keyword(s):  
Wave Equation ◽  
Symbolic Computation ◽  
Wave Solution ◽  
Algebraic Method ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Long Wave

A NEW GENERAL ALGEBRAIC METHOD WITH SYMBOLIC COMPUTATION TO CONSTRUCT NEW TRAVELING SOLUTION FOR THE (1 +1)-DIMENSIONAL DISPERSIVE LONG WAVE EQUATION

2005 ◽  
Vol 16 (07) ◽  
pp. 1107-1119 ◽  
Author(s):  
YONG CHEN
Keyword(s):  
Wave Equation ◽  
Symbolic Computation ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Algebraic Method ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Rational Form ◽  
Wave Solutions ◽  
Long Wave

A new algebraic method, named Riccati equation rational expansion (RERE) method, is devised for constructing multiple traveling wave solutions for nonlinear evolution equations (NEEs). With the aid of symbolic computation, we choose (1 +1)-dimensional dispersive long wave equation (DLWE) to illustrate our method. As a result, we obtain many types of solutions including rational form solitary wave solutions, triangular periodic wave solutions and rational wave solutions.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

scholarly journals New Analytical Solutions of Fractional Symmetric Regularized-Long-Wave Equation

2020 ◽  
Vol 66 (3 May-Jun) ◽  
pp. 297
Author(s):  
Mehmet Senol
Keyword(s):  
Wave Equation ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Algebraic Method ◽  
Symbolic Calculation ◽  
Solution Sets ◽  
Flow Models ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Fractional Differential

In this study, new extended direct algebraic method is successfully implemented to acquire new exact wave solution sets for symmetric regularized-long-wave (SRLW) equation which arise in long water flow models. By the help of Mathematica symbolic calculation package, the method produced a great number of analytical solutions. We also presented a few graphical illustrations for some surfaces. The fractional derivatives are considered in the conformable sense. All of the solutions were checked by substitution to ensure the reliability of the method. Obtained results confirm that the method is straightforward, powerful and effective method to attain exact solutions for nonlinear fractional differential equations. Therefore, the method is a good candidate to take part in the existing literature.

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