scholarly journals A hierarchy of nonlinear evolution equations and finite‐dimensional involutive systems

1994 ◽  
Vol 35 (6) ◽  
pp. 2971-2977 ◽  
Author(s):  
Zhijun Qiao
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Finite Dimensional

Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities

1995 ◽  
Vol 125 (2) ◽  
pp. 225-246 ◽  
Author(s):  
Victor A. Galaktionov
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Invariant Subspaces ◽  
Nonlinear Evolution Equations ◽  
Heat Equations ◽  
Explicit Solutions ◽  
Finite Dimensional ◽  
Quadratic Nonlinearities ◽  
Image Position ◽  
Spatial Operators

We present new explicit solutions to some classes of quasilinear evolution equations arising in different applications, including equations of the Boussinesq type:and quasilinear heat equations:The method is based on construction of finite-dimensional linear functional subspaces which are invariant with respect to spatial operators having quadratic nonlinearities. The corresponding nonlinear evolution equations on invariant subspaces are shown to be equivalent to finite-dimensional dynamical systems. Examples of two-, three- and five- dimensional invariant subspaces are given. Some generalisations to N-dimensional quadratic operators are also considered.

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
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