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

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 Local and Nonlocal Reductions of Two Nonisospectral Ablowitz-Kaup-Newell-Segur Equations and Solutions

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 23
Author(s):  
Hai Jing Xu ◽  
Song Lin Zhao
Keyword(s):  
Gordon Equation ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Jordan Block ◽  
Sine Gordon Equation ◽  
Third Order ◽  
The Third ◽  
Negative Order ◽  
Double Wronskian ◽  
Akns Equation

In this paper, local and nonlocal reductions of two nonisospectral Ablowitz-Kaup-Newell-Segur equations, the third order nonisospectral AKNS equation and the negative order nonisospectral AKNS equation, are studied. By imposing constraint conditions on the double Wronskian solutions of the aforesaid nonisospectral AKNS equations, various solutions for the local and nonlocal nonisospectral modified Korteweg-de Vries equation and local and nonlocal nonisospectral sine-Gordon equation are derived, including soliton solutions and Jordan block solutions. Dynamics of some obtained solutions are analyzed and illustrated by asymptotic analysis.

Soliton Solutions for a Negative Order AKNS Equation Hierarchy

2009 ◽  
Vol 52 (3) ◽  
pp. 395-397 ◽  
Author(s):  
Ji Jie ◽  
Zhang Jian-Bing ◽  
Zhang Da-Jun
Keyword(s):  
Soliton Solutions ◽  
Negative Order ◽  
Akns Equation

scholarly journals Two new Painlev´e integrable KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and new negative-order KdV-CBS equation

2021 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Dispersion Relation ◽  
Soliton Solutions ◽  
Compatibility Conditions ◽  
Multiple Soliton Solutions ◽  
Negative Order ◽  
New Equation

Abstract In this work, we develop two new (3+1)-dimensional KdV–Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and (3+1)-dimensional negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlev´e integrability test via examining the compatibility conditions for each developed model. We examine the dispersion relation and derive multiple soliton solutions for each new equation.

Soliton Solutions for Nonisospectral AKNS Equation by Hirota's Method

2006 ◽  
Vol 45 (3) ◽  
pp. 398-400 ◽  
Author(s):  
Bi Jin-Bo ◽  
Sun Ye-Peng ◽  
Chen Deng-Yuan
Keyword(s):  
Soliton Solutions ◽  
Hirota’S Method ◽  
Akns Equation ◽  
Hirota's Method
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