Titlebook: Solitons; Robin K. Bullough,Philip J. Caudrey Book 1980 Springer-Verlag Berlin Heidelberg 1980 Hamiltonian.atom.differential equation.eige

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Femine

On a Nonlinear Lattice (The Toda Lattice),ns such as multi-soliton state, periodic waves, and solution to the initial value problem by the inverse scattering method. The Bäcklund transformation and the relation to the Korteweg-de Vries equation are also discussed.

Induction

Direct Methods in Soliton Theory, of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form., which we solve exactly using a kind of perturbational approach.

掺和

The Inverse Scattering Transform,n. The close analogy with the ideas of the Fourier transform is emphasized and the general expansions for the unknown functions in terms of the squared eigenfunctions and their derivatives are developed for both eigenvalue problems. The results for the Schrödinger equation are new.. The partial diff

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Hemiplegia

Generalized Matrix Form of the Inverse Scattering Method,s discussed. Second, the inverse scattering method is extended into n × n matrix form. Nonlinear evolution equations which are solvable by the extension are presented. In addition, it is pointed out that the same generalization is possible for discrete cases (lattice problems).

Banister

Nonlinear Evolution Equations Solvable by the Inverse Spectral Transform Associated with the Matrixödinger eigenvalue problem can be extended beyond that described by M. Wadati in the preceding chapter. The most remarkable feature of the novel solvable NEEs thus obtained is the behavior of their solitons, which, while possessing all the stability properties that characterize solitons, generally d

expansive

幼儿

Quantum Solitons in Statistical Physics, reviews the interrelationships between these models, their formulation, and the operators which describe them. The common denominator is the quantum sine-Gordon model, which is reduced to solvable form. The solution for the eigenvalue spectrum is discussed, and the equivalence of solitons, particle

令人作呕

The Soliton and Its History,emaining chapters. The differential geometry of one large class of nonlinear evolution equations is described. Some connections with nonlinear field theories and with solvable many-body problems are established. The short biography of John Scott Russell which forms much of the first section is continued as an appendix at the back of this volume.