The bi‐Hamiltonian structure for the restricted flows of the Boussinesq and the modified Boussinesq equation

1993 ◽  
Vol 34 (10) ◽  
pp. 4742-4754 ◽  
Author(s):  
Yunbo Zeng
Keyword(s):  
Hamiltonian Structure ◽  
Boussinesq Equation ◽  
Modified Boussinesq Equation

A FRACTIONAL KdV HIERARCHY

1991 ◽  
Vol 06 (17) ◽  
pp. 1561-1573 ◽  
Author(s):  
IOANNIS BAKAS ◽  
DIDIER A. DEPIREUX
Keyword(s):  
Hamiltonian Structure ◽  
Boussinesq Equation ◽  
Operator Algebras ◽  
Nonlinear Differential Equations ◽  
Conserved Quantities ◽  
Gauge Groups ◽  
Yang Mills ◽  
Kdv Hierarchy ◽  
Alternative Set ◽  
New System

We construct a new system of integrable nonlinear differential equations associated with. the operator algebra [Formula: see text] of Polyakov. Its members are fractional generalizations of KdV type flows corresponding to an alternative set of constraints on the 2-dim. SL(3) gauge connections. We obtain the first non-trivial examples by dimensional reductiion from self-dual Yang–Mills and then generate recursively the entire hierarchy and its conserved quantities using a bi-Hamiltonian structure. Certain relations with the Boussinesq equation are also discussed together with possible generalizations of the formalism to SL (N) gauge groups and [Formula: see text] operator algebras with arbitrary N and l.

scholarly journals N = 2 SUPER W3 ALGEBRA AND N = 2 SUPER BOUSSINESQ EQUATIONS

1995 ◽  
Vol 10 (02) ◽  
pp. 253-288 ◽  
Author(s):  
E. IVANOV ◽  
S. KRIVONOS ◽  
R.P. MALIK
Keyword(s):  
Hamiltonian Structure ◽  
Boussinesq Equation ◽  
Boussinesq Equations ◽  
Geometric Interpretation ◽  
Nonlinear Realization ◽  
Linear Formula ◽  
Reduction Approach

We study classical N=2 super W3 algebra and its interplay with N=2 supersymmetric extensions of the Boussinesq equation in the framework of the nonlinear realization method and the inverse Higgs-covariant reduction approach. These techniques have been previously used by us in the bosonic W3 case to give a new geometric interpretation of the Boussinesq hierarchy. Here we deduce the most general N=2 super Boussinesq equation and two kinds of the modified N=2 super Boussinesq equations, as well as the super Miura maps relating these systems to each other, by applying the covariant reduction to certain coset manifolds of linear [Formula: see text] symmetry associated with N=2 super W3. We discuss the integrability properties of the equations obtained and their correspondence with the formulation based on the notion of the second Hamiltonian structure.

scholarly journals An application of the MEFM to the modified Boussinesq equation

2018 ◽  
Vol 9 (1) ◽  
pp. 11-17
Author(s):  
Tolga Akturk
Keyword(s):  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
3D Graphics ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Wolfram Mathematica ◽  
Modified Boussinesq Equation ◽  
Mathematica Software ◽  
2D And 3D

In this paper, some travelling wave solutions of the Modified Boussinesq (MBQ) equation are obtained by using the modified expansion function method (MEFM). When the obtained solutions are commented, trigonometric functions including hyperbolic features are obtained. The 2D and 3D graphics of the solutions have been investigated by selecting appropriate parameters. All the obtained solutions provide the MBQ equation. In this work, all mathematical calculations are done with Wolfram Mathematica software. 

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