scholarly journals A COMMENT ON THE ODD FLOWS FOR THE SUPERSYMMETRIC KdV EQUATION

1994 ◽  
Vol 09 (35) ◽  
pp. 3235-3243 ◽  
Author(s):  
EDUARDO RAMOS
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Two Dimensional ◽  
Kp Hierarchy ◽  
Additional Symmetries ◽  
Type Reduction ◽  
Lax Operator ◽  
Nonlocal Conservation Laws ◽  
Fourth Root ◽  
Supersymmetric Kdv Equation

In a recent paper Dargis and Mathieu introduced integrodifferential odd flows for the supersymmetric KdV equation. These flows are obtained from the nonlocal conservation laws associated with the fourth root of its Lax operator. In this note I show that only half of these flows are of the standard Lax form, while the remaining half provide us with Hamiltonians for an SKdV-type reduction of a new supersymmetric hierarchy. This new hierarchy is shown to be closely related to the Jacobian supersymmetric KP-hierarchy of Mulase and Rabin. A detailed study of the algebra of additional symmetries of this new hierarchy reveals that it is isomorphic to the super-W1+∞ algebra, thus making it a candidate for a possible interrelationship between superintegrability and two-dimensional supergravity.

On the solutions and conservation laws of a two-dimensional Korteweg de Vries model: Multiple exp-function method

2018 ◽  
Vol 24 (1) ◽  
pp. 27-33 ◽  
Author(s):  
Abdullahi Rashid Adem
Keyword(s):  
Conservation Laws ◽  
Infinite Number ◽  
Function Method ◽  
Soliton Solutions ◽  
Two Dimensional ◽  
De Vries ◽  
Nonlocal Conservation Laws ◽  
Exact Soliton Solutions

AbstractUnder investigation in this paper is a two-dimensional Korteweg de Vries model, which is a spacial extension of the Korteweg de Vries model. An infinite number of nonlocal conservation laws are given which indicate the integrability of this model. Exact soliton solutions are then respectively derived by means of the multiple exp-function method.

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

Sign in / Sign up

Export Citation Format

Share Document