scholarly journals Using trial equation method to solve the exact solutions for two kinds of KdV equations with variable coefficients

2005 ◽  
Vol 54 (10) ◽  
pp. 4506
Author(s):  
Liu Cheng-Shi
Keyword(s):  
Exact Solutions ◽  
Variable Coefficients ◽  
Equation Method ◽  
Trial Equation Method ◽  
Kdv Equations

Exact Solutions to Zakharov-Kuznetsov Equation with Variable Coefficients by Trial Equation Method

2017 ◽  
Vol 73 (1) ◽  
pp. 1-4 ◽  
Author(s):  
Shu Yang
Keyword(s):  
Periodic Solution ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Variable Coefficients ◽  
Equation Method ◽  
Polynomial Method ◽  
Rational Solutions ◽  
Trial Equation Method ◽  
Solitary Solutions ◽  
Complete Discrimination System

AbstractBy the trial equation method and the complete discrimination system for polynomial method, some exact solutions to Zakharov-Kuznetsov equation with variable coefficients are obtained. These solutions include solitary solutions, rational solutions, periodic solution and double periodic solutions.

scholarly journals Soliton solutions of coupled higgs field equation via the trial equation method

2019 ◽  
Vol 7 (2) ◽  
pp. 106
Author(s):  
S. Subhaschandra Singh
Keyword(s):  
Field Equation ◽  
Exact Solutions ◽  
Particle Physics ◽  
Soliton Solutions ◽  
Higgs Field ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
Fibre Optics ◽  
Trial Equation Method ◽  
Coupled Equation

Since a few recent decades, investigation of nonlinear evolution equations (NLEEs) is becoming an important area of research as they have a variety of applications in various branches of social and scientific disciplines like Ecology, Social Dynamics, Financial Mathematics, Engineering and many branches of Physics such as Biophysics, Chemical Physics, Fibre Optics, Fluid Mechanics, Neuro-physics, Particle Physics, Solid State Physics and many more. Many powerful and efficient methods of finding exact solutions of NLEEs have been proposed so far and the Trial Equation Method [ 1 - 5] is one of them. Many authors have successfully used the method in finding exact solutions of a number of NLEEs. In the present paper, soliton solutions of the Coupled Higgs Field Equation [ 6 - 10 ] are being obtained using the Trial Equation Method. The Coupled Higgs Field Equation describes system of conserved scalar nucleons interacting with neutral scalar mesons in particle physics. This coupled equation has applications in the studies of Field Theory and Electromagnetic waves as well. This coupled equation introduces the Higgs field to illustrate the mechanism of generation of mass for Gauge Bosons. The Coupled Higgs Field Equation is generally expressed as the following pair of NLEEs                                                                                                                                                          (3) and                                                                                                                                                                          (2) Here, x and t are spatial and temporal variables respectively, the function  is a complex scalar nucleon field, the function  is a real scalar meson field,  are arbitrary real constants and the subscripts denote partial differentiations with respect to them.Using the Trial Equation Method, the above coupled NLEE is to be solved to obtain some soliton solutions.

scholarly journals AKNS Formalism and Exact Solutions of KdV and Modified KdV Equations with Variable-Coefficients

2016 ◽  
Vol 6 ◽  
pp. 32-41 ◽  
Author(s):  
Supratim Das ◽  
Dibyendu Ghosh
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Elliptic Functions ◽  
Variable Coefficients ◽  
Jacobian Elliptic Functions ◽  
Generalized Kdv Equation ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Modified Kdv Equation ◽  
Modified Kdv Equations

We apply the AKNS hierarchy to derive the generalized KdV equation andthe generalized modified KdV equation with variable-coefficients. We system-atically derive new exact solutions for them. The solutions turn out to beexpressible in terms of doubly-periodic Jacobian elliptic functions.

scholarly journals Exact dynamical behavior for a dual Kaup–Boussinesq system by symmetry reduction and coupled trial equations method

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Wen-He Li ◽  
Yong Wang
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Propagation Velocity ◽  
Dynamical Behavior ◽  
Symmetry Reduction ◽  
Equation Method ◽  
Boussinesq System ◽  
Invariant Property ◽  
Function Solution ◽  
Trial Equation Method

Abstract We propose a coupled trial equation method for a coupled differential equations system. Furthermore, according to the invariant property under the translation, we give the symmetry reduction of a dual Kaup–Boussinesq system, and then we use the proposed trial equation method to construct its exact solutions which describe its dynamical behavior. In particular, we get a cosine function solution with a constant propagation velocity, which shows an important periodic behavior of the system.

scholarly journals On the exact solutions of the fractional (2+1)- dimensional Davey - Stewartson equation system

2017 ◽  
Vol 7 (3) ◽  
pp. 265-270
Author(s):  
Gülnur Yel ◽  
Zeynep Fidan Koçak
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Trigonometric Function ◽  
Equation Method ◽  
Exact Traveling Wave Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this work, we construct the exact traveling wave solutions of the fractional (2+1)-dimensional Davey-Stewartson equation system (D-S) that is complex equation system using the Modified Trial Equation Method (MTEM). We obtained trigonometric function solutions by this method that are new in literature.

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