Fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equation

2013 ◽  
Vol 54 (3) ◽  
pp. 033506 ◽  
Author(s):  
Zhao-Wen Yan ◽  
Min-Li Li ◽  
Ke Wu ◽  
Wei-Zhong Zhao
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Structure Theory ◽  
Prolongation Structure

Fermionic covariant prolongation structure theory for a (2+1)-dimensional super nonlinear evolution equation

2018 ◽  
Vol 15 (07) ◽  
pp. 1850114 ◽  
Author(s):  
Zhaowen Yan ◽  
Chuanzhong Li
Keyword(s):  
Evolution Equation ◽  
Integrable System ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Structure Theory ◽  
Backlund Transformation ◽  
Prolongation Structure ◽  
New Formula

In the framework of the fermionic covariant prolongation structure theory (PST), we investigate the integrability of a new [Formula: see text]-dimensional super nonlinear evolution equation (NEE). The prolongation structure of the super integrable system is presented. Moreover, we derive the Bäcklund transformation of the super integrable system.

The prolongation structures of quasi-polynomial flows

1983 ◽  
Vol 385 (1789) ◽  
pp. 389-429 ◽  
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Linear Representation ◽  
Second Step ◽  
Free Lie Algebra ◽  
Finite Dimensional ◽  
Algebraic Framework ◽  
Prolongation Structure ◽  
Polynomial Flows

We look closely at the process of finding a Wahlquist-Estabrook prolongation structure for a given (system of) nonlinear evolution equation(s). There are two main steps in this calculation: the first, to reduce the problem to the investigation of a finitely generated, free Lie algebra with constraints; the second, to find a finite-dimensional linear representation of these generators. We discuss some of the difficulties that arise in this calculation. For quasi-polynomial flows (defined later) we give an algorithm for the first step. We do not totally solve the problems of the second step, but do give an algebraic framework and a number of techniques that are quite generally applicable. We illustrate these methods with many examples, several of which are new.

scholarly journals Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

Sign in / Sign up

Export Citation Format

Share Document