scholarly journals New Exact Solutions for the Variable Coefficient Two-Dimensional Burger Equation

2012 ◽  
Vol 2 (1) ◽  
pp. 21-24
Author(s):  
Rehab M. El -Shiekh
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Burger Equation ◽  
Two Dimensional ◽  
New Exact Solutions

scholarly journals New Classes of Solutions of Dynamical Problems of Plasticity

2020 ◽  
pp. 792-796
Author(s):  
Sergei I. Senashov ◽  
Olga V. Gomonova ◽  
Irina L. Savostyanova ◽  
Olga N. Cherepanova
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Plastic Layer ◽  
Two Dimensional ◽  
Science And Engineering ◽  
Spatial Variables ◽  
One Dimensional ◽  
New Exact Solutions

Dynamical problems of the theory of plasticity have not been adequately studied. Dynamical problems arise in various fields of science and engineering but the complexity of original differential equations does not allow one to construct new exact solutions and to solve boundary value problems correctly. One-dimensional dynamical problems are studied rather well but two-dimensional problems cause major difficulties associated with nonlinearity of the main equations. Application of symmetries to the equations of plasticity allow one to construct some exact solutions. The best known exact solution is the solution obtained by B.D. Annin. It describes non-steady compression of a plastic layer by two rigid plates. This solution is a linear one in spatial variables but includes various functions of time. Symmetries are also considered in this paper. These symmetries allow transforming exact solutions of steady equations into solutions of non-steady equations. The obtained solution contains 5 arbitrary functions

scholarly journals Variable-Coefficient Exact Solutions for Nonlinear Differential Equations by a New Bernoulli Equation-Based Subequation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Chunxia Qi ◽  
Shunliang Huang
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Variable Coefficient ◽  
Nonlinear Differential Equations ◽  
Bernoulli Equation ◽  
New Exact Solutions

A new Bernoulli equation-based subequation method is proposed to establish variable-coefficient exact solutions for nonlinear differential equations. For illustrating the validity of this method, we apply it to the asymmetric (2 + 1)-dimensional NNV system and the Kaup-Kupershmidt equation. As a result, some new exact solutions with variable functions coefficients for them are successfully obtained.

New exact solutions for a generalized variable-coefficient KdV equation

2008 ◽  
Vol 69 (8) ◽  
pp. 2763-2770 ◽  
Author(s):  
R. Sabry ◽  
W.F. El-Taibany
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Kdv Equation ◽  
New Exact Solutions

Non-linear Dynamics and Exact Solutions for the Variable-Coefficient Modified Korteweg–de Vries Equation

2018 ◽  
Vol 73 (2) ◽  
pp. 143-149 ◽  
Author(s):  
Jiangen Liu ◽  
Yufeng Zhang
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Rational Solutions ◽  
Transformation Technique ◽  
Linear Dynamics ◽  
New Exact Solutions ◽  
Non Linear ◽  
De Vries

AbstractThis paper presents some new exact solutions which contain soliton solutions, breather solutions and two types of rational solutions for the variable-coefficient-modified Korteweg–de Vries equation, with the help of the multivariate transformation technique. Furthermore, based on these new soliton solutions, breather solutions and rational solutions, we discuss their non-linear dynamics properties. We also show the graphic illustrations of these solutions which can help us better understand the evolution of solution waves.

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