Lax pairs, recursion operators and the perturbation of nonlinear evolution equations

1991 ◽  
pp. 53-60
Author(s):  
Russell Herman
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Recursion Operators ◽  
Lax Pairs

scholarly journals Multicomponent Nonlinear Evolution Equations of the Heisenberg Ferromagnet Type: Local Versus Nonlocal Reductions

2021 ◽  
pp. 274-285
Author(s):  
Tihomir Valchev
Keyword(s):  
Heisenberg Model ◽  
Symmetric Spaces ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Heisenberg Ferromagnet ◽  
Lax Pairs ◽  
Hermitian Symmetric Spaces ◽  
Integrable Deformation

This work is dedicated to systems of matrix nonlinear evolution equations related to Hermitian symmetric spaces of the type $\mathbf{A.III}$. The systems under consideration generalize the $1+1$ dimensional Heisenberg ferromagnet equation in the sense that their Lax pairs are linear bundles in pole gauge like for the original Heisenberg model. Here we present certain local and nonlocal reductions. A local integrable deformation and some of its reductions are discussed as well.

scholarly journals Scaling invariant Lax pairs of nonlinear evolution equations

2012 ◽  
Vol 91 (2) ◽  
pp. 381-402 ◽  
Author(s):  
Mark Hickman ◽  
Willy Hereman ◽  
Jennifer Larue ◽  
Ünal Göktaş
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Lax Pairs ◽  
Scaling Invariant

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.

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