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Polynomial conserved densities for the sine-Gordon equations

- R. Dodd, R. Bullough
- MathematicsProceedings of the Royal Society of London. A…
- 4 February 1977

Like a number of other nonlinear dispersive wave equations the sine–Gordonequation z, xt = sin z has both multi-soliton solutions and an infinity of conserved densities which are polynomials in z,x,… Expand

Exact solution of generalized Tavis - Cummings models in quantum optics

- N. Bogoliubov, R. Bullough, J. Timonen
- Physics
- 7 October 1996

Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number… Expand

Bäcklund transformations for the sine–Gordon equations

- R. Dodd, R. Bullough
- MathematicsProceedings of the Royal Society of London. A…
- 8 December 1976

The generalized sine–Gordon equations z,xt = F(z) in two independent variables x, t include the sine–Gordon z,xt = sin z and the multiple sine–Gordon’s like z,xt = sin z + ½ sin ½z. Among other… Expand

A q-deformed completely integrable Bose gas model

- N. Bogoliubov, R. Bullough
- Physics
- 21 July 1992

The authors construct the Hamiltonian of a new quantum integrable 'q-boson' lattice model in 1+1 dimensions which has q-bosons as dynamical variables and solve it for its energy eigenstates and… Expand

Geometry of the akns — ZS inverse scattering scheme

- R. Sasaki, R. Bullough
- Mathematics
- 1980

We review the geometrical theory of nonlinear evolution equations (NEEs) solvable by the AKNS1-generalised Zakharov-Shabat2 scattering problem introduced by one of us previously3,4. We show how the… Expand

Solitons in nonlinear optics. I. A more accurate description of the 2π pulse in self-induced transparency

- J. C. Eilbeck, J. Gibbon, P. Caudrey, R. Bullough
- Physics
- 1 September 1973

A more accurate description of the 2 pi pulse of self-induced transparency is obtained. This is an exact solution of an approximate form of the Maxwell-Bloch equations in which only backscattering is… Expand

A general theory of self-induced transparency

- R. Bullough, P. Caudrey, J. C. Eilbeck, J. Gibbon
- Physics
- 1974

We summarize a theory of self-induced transparency (SIT) which exhibits so-called ‘soliton’ solutions of the underlying equations, as the natural description of pulse evolution and break up. The… Expand

“The Wave” “Par Excellence”, the Solitary Progressive Great Wave of Equilibrium of the Fluid: An Early History of the Solitary Wave

- R. Bullough
- Physics
- 1988

It is shown how in 1876 Rayleigh resolved the conflict between Russell on the one hand, and Stokes and Airy on the other, about the nature of the solitary wave and the formula for its velocity of… Expand

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