A class of nonlinear evolution equations subjected to nonlocal initial conditions

2010 ◽  
Vol 72 (11) ◽  
pp. 4091-4100 ◽  
Author(s):  
Angela Paicu ◽  
Ioan I. Vrabie
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Initial Conditions ◽  
Nonlinear Evolution Equations ◽  
Nonlocal Initial Conditions

Role of parabolic viscosity in numerical analysis of derivative nonlinear evolution equations

1998 ◽  
Vol 2 ◽  
pp. 75-80
Author(s):  
Tadas Meškauskas ◽  
Feliksas Ivanauskas
Keyword(s):  
Numerical Analysis ◽  
Nonlinear System ◽  
Boundary Value Problem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Initial Conditions ◽  
Nonlinear Evolution Equations ◽  
Complex Vector ◽  
The Difference

We consider the difference schemes applied to a derivative nonlinear system of evolution equations. For the boundary-value problem with initial conditions ∂u/∂t = A ∂2u/∂x2 + B ∂u/∂x + f(x,u) + g(x,u) ∂u/∂x,    (t,x) ∈  (0, T] x (0, 1),u(t,0) = u(t,1) = 0,    t ∈ [0, T],u(0,x) = u(0)(x),    x ∈ (0, 1) we use the Crank-Nicolson discretization. A is complex and B – real diagonal matrixes; u, f and g are complex vector-functions. The analysis shows that proposed schemes are uniquely solvable, convergent and stable in a grid norm W22 if all (diagonal) elements in Re(A) are positive. This is true without any restriction on the ratio of time and space grid steps.

scholarly journals An Efficient Method for Solving Coupled Time Fractional Nonlinear Evolution Equations with Conformable Fractional Derivatives

2020 ◽  
pp. 3071-3083
Author(s):  
Osama H. Mohammed ◽  
Firas S. Ahmed
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Initial Conditions ◽  
Time Derivative ◽  
Approximate Solutions ◽  
Nonlinear Evolution Equations ◽  
Diffusion Reaction ◽  
Power Series Method ◽  
Coupled Diffusion ◽  
Fractional Time Derivative

In this article, an efficient reliable method, which is the residual power series method (RPSM), is used in order to investigate the approximate solutions of conformable time fractional nonlinear evolution equations with conformable derivatives under initial conditions. In particular, two types of equations are considered, which are time coupled diffusion-reaction equations (CD-REs) and MKdv equations coupled with conformable fractional time derivative of order α. The attitude of RPSM and the influence of different values of α are shown graphically.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method

scholarly journals Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions

1998 ◽  
Vol 39 (7) ◽  
pp. 3765-3771 ◽  
Author(s):  
M. Lakshmanan ◽  
R. Myrzakulov ◽  
S. Vijayalakshmi ◽  
A. K. Danlybaeva
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Curves And Surfaces

New Integrable Nonlinear Evolution Equations

1979 ◽  
Vol 47 (5) ◽  
pp. 1698-1700 ◽  
Author(s):  
Miki Wadati ◽  
Kimiaki Konno ◽  
Yoshi H. Ichikawa
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations
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