Canonical equations of Hamilton for the nonlinear Schrödinger equation

@article{Liang2013CanonicalEO,
  title={Canonical equations of Hamilton for the nonlinear Schr{\"o}dinger equation},
  author={Guo Liang and Qi Guo and Zhanmei Ren},
  journal={Journal of Physics: Conference Series},
  year={2013},
  volume={633}
}
We define two different systems of mathematical physics: the second order differential system (SODS) and the first order differential system (FODS). The Newton's second law of motion and the nonlinear Schrödinger equation (NLSE) are the exemplary SODS and FODS, respectively. We obtain a new kind of canonical equations of Hamilton (CEH), which exhibit some kind of symmetry in form and are formally different from the conventional CEH without symmetry [H. Goldstein, C. Poole, J. Safko, Classical… 
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References

SHOWING 1-10 OF 15 REFERENCES

Nonlinear band structure in Bose-Einstein condensates: Nonlinear Schrödinger equation with a Kronig-Penney potential

All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one-dimensional lattice are presented in closed analytic form. The band structure is investigated by analyzing

Stability of periodic waves of finite amplitude on the surface of a deep fluid

We study the stability of steady nonlinear waves on the surface of an infinitely deep fluid [1, 2]. In section 1, the equations of hydrodynamics for an ideal fluid with a free surface are transformed

Dissipative Solitons in the Complex Ginzburg-Landau and Swift Hohenberg Equations

We explain the meaning of dissipative solitons and place them in a framework which shows their use in various scientific fields. Indeed, dissipative solitons form a new paradigm for the investigation

Physics of Solitons

List of Portraits Preface Part I. Different Classes of Solitons: Introduction 1. Nontopological solitons: the Korteweg-de Vries equation 2. Topological soltitons: sine-Gordon equation 3. Envelope

Mathematics for physicists

1. Describing the Universe. 2. Complex Variables. 3. Differential Equations. 4. Fourier Series. 5. Laplace Transforms. 6. Generalized Functions in Physics. 7. Fourier Transforms. 8. The

Mathematical Methods for Physicists

Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations.

Nonlinear Fiber Optics

Nonlinear fiber optics concerns with the nonlinear optical phenomena occurring inside optical fibers. Although the field ofnonlinear optics traces its beginning to 1961, when a ruby laser was first

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Variational approach to nonlinear pulse propagation in optical fibers

The problem of nonlinear pulse propagation in optical fibers, as governed by the nonlinear Schr\"odinger equation, is reformulated as a variational problem. By means of Gaussian trial functions and a