## 226 Citations

Ja n 20 09 INVOLUTIVE DISTRIBUTIONS OF OPERATOR-VALUED EVOLUTIONARY VECTOR FIELDS

- Mathematics
- 2021

Converting a pioneering idea of V. V. Sokolov et al. [60] to a geometric object, we introduce a well-defined notion of linear matrix operators in total derivatives, whose images in the Lie algebras g…

Traces on the cone algebra with asymptotics

- Mathematics
- 1996

For every singular point on a manifold with conical singularities we construct a trace on the 'Cone Algebra with Asymptotics introduced by B.-W. Schulze. Each of these traces is determined at the…

Multi-soliton solutions and quasi-periodic solutions of nonlinear equations of sine-Gordon type

- Mathematics
- 1983

In part I of this paper we construct multi-soliton solutions of these equations and some related nonlinear equations. In part II, we construct quasi-periodic solutions by using the abelian integrals.…

Multisoliton solutions and quasiperiodic solutions of nonlinear equations of sine-Gordon type

- Mathematics
- 1982

Modifying Lax equations and the second Hamiltonian structure

- Mathematics
- 1980

where P+ is a differential operator whose coefficients are differential polynomials in u, that is, polynomials in u and its x-derivatives u (s~. (The subscript + may be ignored at this point: we…

VARIATIONAL DERIVATION OF THE GREEN–NAGHDI SHALLOW-WATER EQUATIONS

- Mathematics
- 2012

We consider the two-dimensional irrotational water-wave problem with a free surface and a flat bottom. In the shallow-water regime and without smallness assumption on the wave amplitude we derive, by…

A Two Dimensional Adler-Manin Trace and Bi-singular Operators

- Mathematics
- 2011

Motivated by the theory of bi-singular pseudodifferential operators, we introduce a two dimensional version of the Adler-Manin trace. Our construction is rather general in the sense that it involves…

The Algebra of Formal Twisted Pseudodifferential Symbols and a Noncommutative Residue

- Mathematics
- 2008

Motivated by Connes–Moscovici’s notion of a twisted spectral triple, we define an algebra of formal twisted pseudodifferential symbols with respect to a twisting of the base algebra. We extend the…

Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary

- Mathematics
- 2007

We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary.…

Discrete lax equations and differential-difference calculus

- Mathematics
- 1985

Lax equations of Chapter I. Namely, by putting rk(x.) = aj, deg(x q »x. fd ) = k, we find that rk = 0#deg w and so the condition w(8p) = 0 in 1(1.26) is equivalent to rk(8. P = ß degOJ, which is ßn…

## References

SHOWING 1-10 OF 36 REFERENCES

Hill’s Operator and Hyperelliptic Function Theory in the Presence of Infinitely Many Branch Points

- Mathematics
- 1976

\(C_{1}^{k},\,k \leq \infty \), is the class of k times continuously differentiable real-valued functions of period 1. Q denotes the Hill’s operator − d2∕dx2 + q(x) with a fixed q of class…

The soliton: A new concept in applied science

- Physics
- 1973

The term soliton has recently been coined to describe a pulselike nonlinear wave (solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed. To date at least…

A Variety of Nonlinear Network Equations Generated from the Bäcklund Transformation for the Toda Lattice

- Mathematics, Physics
- 1976

A Backlund transformation in the bilinear form is presented for the Toda equation. The Backlund transformation generates an important class of nonlinear evolution equations that exhibits N-soliton…

Integrable Hamiltonian systems and interactions through quadratic constraints

- Physics, Mathematics
- 1976

On-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable…

Some comments on the many-dimensional solitons

- Physics
- 1976

The possibilities for the existence of truly localized soliton solutions in the realistic three-dimensional case are discussed. The gauge invariant theory of a non-linear chiral field is shown to be…

The Korteweg–deVries Equation: A Survey of Results

- Physics, Mathematics
- 1976

The Korteweg–de Vries equation \[ u_t + uu_x + u_{xxx} = 0\] is a nonlinear partial differential equation arising in the study of a number of different physical systems, e.g., water waves, plasma…

Topological Charges in Field Theory

- Mathematics, Physics
- 1976

Non-dynamical conserved quantities are analysed for a class of field theories and their topological character is discussed. Some examples are given.