Noncommutative negative order AKNS equation and its soliton solutions

2018 ◽  
Vol 33 (35) ◽  
pp. 1850209 ◽  
Author(s):  
H. Wajahat A. Riaz ◽  
Mahmood ul Hassan
Keyword(s):  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Infinite Sequence ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Curvature Condition ◽  
Integrable Structure ◽  
Zero Curvature ◽  
Negative Order ◽  
Akns Equation

A noncommutative negative order AKNS (NC-AKNS(-1)) equation is studied. To show the integrability of the system, we present explicitly the underlying integrable structure such as Lax pair, zero-curvature condition, an infinite sequence of conserved densities, Darboux transformation (DT) and quasideterminant soliton solutions. Moreover, the NC-AKNS(-1) equation is compared with its commutative counterpart not only on the level of nonlinear evolution equation but also for the explicit solutions.

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.

Soliton Solutions for a Negative Order AKNS Equation

2008 ◽  
Vol 50 (5) ◽  
pp. 1033-1035 ◽  
Author(s):  
Ji Jie ◽  
Zhao Song-Lin ◽  
Zhang Da-Jun
Keyword(s):  
Soliton Solutions ◽  
Negative Order ◽  
Akns Equation

scholarly journals Soliton Solutions and Conservation Laws of a (3+1)-Dimensional Nonlinear Evolution Equation

2019 ◽  
Vol 135 (3) ◽  
pp. 539-545
Author(s):  
M. Ekici ◽  
A. Sonmezoglu ◽  
A. Rashid Adem ◽  
Qin Zhou ◽  
Zitong Luan ◽  
...  
Keyword(s):  
Evolution Equation ◽  
Conservation Laws ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions

The Properties of Bilinear Derivative

2014 ◽  
Vol 543-547 ◽  
pp. 1905-1908
Author(s):  
Ju Mei Zhang ◽  
Hong Lun Wang ◽  
Wen Yan Cui
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Learning And Teaching ◽  
Derivative Method ◽  
Nonlinear Science ◽  
Definition Of

Bilinear derivative method is widely used in calculating multi-soliton solutions of some nonlinear evolution equation. The paper proves some frequently used properties of bilinear derivative from the perspective of the definition of bilinear derivative, hoping to be useful for learning and teaching in nonlinear science.

Travelling Wave Solutions of Nonlinear Evolution Equation by Using an Auxiliary Elliptic Equation Method

2012 ◽  
Vol 166-169 ◽  
pp. 3228-3232 ◽  
Author(s):  
Chun Huan Xiang
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Nonlinear Differential Equations ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Equation Method ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Dispersive Waves

The Camassa-Holm and Degasperis-Procesi equation describing unidirectional nonlinear dispersive waves in shallow water is reconsidered by using an auxiliary elliptic equation method. Detailed analysis of evolution solutions of the equation is presented. Some entirely new periodic-soliton solutions, include Jacobi elliptic function solutions, hyperbolic solutions and trigonal solutions, are obtained. The employed auxiliary elliptic equation method is powerful and can be also applied to solve other nonlinear differential equations. This method adds a new route to explore evolution solutions of nonlinear differential equation.

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