A Geometric Study of the Dispersionless Boussinesq Type Equation

@article{Kersten2006AGS,
  title={A Geometric Study of the Dispersionless Boussinesq Type Equation},
  author={P. H. M. Kersten and Iosif Krasil’shchik and Alexander Verbovetsky},
  journal={Acta Applicandae Mathematica},
  year={2006},
  volume={90},
  pages={143-178}
}
We discuss the dispersionless Boussinesq type equation, which is equivalent to the Benney–Lax equation, being a system of equations of hydrodynamical type. This equation was discussed in [4]. The results include: A description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws (cosymmetries). Highly interesting are the appearances of operators… 

Homogeneous Hamiltonian operators and the theory of coverings

Integrable structures for a generalized Monge-Ampère equation

We consider a third-order generalized Monge-Ampère equation uyyy − uxxy2 + uxxxuxyy = 0, which is closely related to the associativity equation in two-dimensional topological field theory. We

On Integrability of the Camassa–Holm Equation and Its Invariants

Using geometrical approach exposed in (Kersten et al. in J. Geom. Phys. 50:273–302, [2004] and Acta Appl. Math. 90:143–178, [2005]), we explore the Camassa–Holm equation (both in its initial scalar

Conservation Laws and Nonlocal Variables

We discuss here the notion of conservation laws and briefly the theory of Abelian coverings over infinitely prolonged equations. Computation of conservation laws is also closely related to that of

Pre-Hamiltonian structures for integrable nonlinear systems

Pre-Hamiltonian matrix operators in total derivatives are considered; they are defined by the property that their images are subalgebras of the Lie algebra of evolutionary vector fields. This

Geometry of jet spaces and integrable systems

The Bilinear Integrability, N-soliton and Riemann-theta function solutions of B-type KdV Equation

In this paper, the bilinear integrability for B-type KdV equation have been explored. According to the relation to tau function, we find the bilinear transformation and construct the bilinear form

Quasilinear Systems of First Order PDEs with Nonlocal Hamiltonian Structures

In this paper we investigate whether a quasilinear system of PDEs of first order admits Hamiltonian formulation with local and nonlocal operators. By using the theory of differential coverings, we

Operator-valued involutive distributions of evolutionary vector fields and their affine geometry

Involutive distributions of evolutionary vector fields that belong to images of matrix operators in total derivatives are considered and some classifications of the operators are obtained. The weak

References

SHOWING 1-10 OF 20 REFERENCES

Bi-Hamiltonian structures of d-Boussinesq and Benney-Lax equations

The dispersionless-Boussinesq and Benney-Lax equations are equations of hydrodynamic type which can be obtained as reductions of the dispersionless Kadomtsev-Petviashvili equation. We find that for

(Non)local Hamiltonian and symplectic structures, recursions and hierarchies: a new approach and applications to the N = 1 supersymmetric KdV equation

Using methods of Kersten et al (2004 J. Geom. Phys. 50 273–302) and Krasil'shchik and Kersten (2000 Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations

On the formalism of local variational differential operators

The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free

Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations

The theory of coverings over differential equations is exposed which is an adequate language for describing various nonlocal phenomena: nonlocal symmetries and conservation laws, Bäcklund

Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations

Preface. 1. Classical symmetries. 2. Higher symmetries and conservation laws. 3. Nonlocal theory. 4. Brackets. 5. Deformations and recursion operators. 6. Super and graded theories. 7. Deformations

Homological Methods in Equations of Mathematical Physics

These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the

On the Integrability Conditions for Some Structures Related to Evolution Differential Equations

Using the result by D. Gessler, we show that any invariant variational bivector (resp., variational 2-form) on an evolution equation with nondegenerate right-hand side is Hamiltonian (resp.,

Symmetries and conservation laws for differential equations of mathematical physics

Ordinary differential equations First-order equations The theory of classical symmetries Higher symmetries Conservation laws Nonlocal symmetries From symmetries of partial differential equations