• Corpus ID: 221090115

On the nonlinear Schr\"odinger equation with a time-dependent boundary condition.

@article{Xia2020OnTN,
  title={On the nonlinear Schr\"odinger equation with a time-dependent boundary condition.},
  author={Baoqiang Xia},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2020}
}
  • B. Xia
  • Published 10 August 2020
  • Mathematics
  • arXiv: Exactly Solvable and Integrable Systems
We study the nonlinear Schrodinger equation on the half-line with a boundary condition that involves time derivative. This boundary condition was presented by Zambon [J. High Energ. Phys. 2014 (2014) 36]. We establish the integrability of such a boundary both by using the Sklyanin's formalism and by using the tool of Backlund transformations together with a suitable reduction of reflection type. Moreover, we present a method to derive explicit formulae for multi-soliton solutions of the… 

References

SHOWING 1-10 OF 20 REFERENCES

On the Nonlinear Schrödinger Equation on the Half Line with Homogeneous Robin Boundary Conditions

Boundary value problems for the nonlinear Schrödinger equations on the half line with homogeneous Robin boundary conditions are revisited using Bäcklund transformations. In particular: relations are

The classical nonlinear Schrödinger model with a new integrable boundary

A bstractA new integrable boundary for the classical nonlinear Schrödinger model is derived by dressing a boundary with a defect. A complete investigation of the integrability of the new boundary is

Solitons, boundary value problems and a nonlinear method of images

We characterize the soliton solutions of the nonlinear Schrödinger equation on the half-line with linearizable boundary conditions. Using an extension of the solution to the whole line and the

Dressing the boundary: On soliton solutions of the nonlinear Schrödinger equation on the half‐line

  • C. Zhang
  • Mathematics, Physics
    Studies in Applied Mathematics
  • 2019
Based on the theory of integrable boundary conditions (BCs) developed by Sklyanin, we provide a direct method for computing soliton solutions of the focusing nonlinear Schrödinger equation on the

Boundary conditions for integrable equations

The problem of constructing boundary conditions for nonlinear equations compatible with higher symmetries is considered. In particular, this problem is discussed for the sine - Gordon, Jiber -

Jump-defects in the nonlinear Schrödinger model and other non-relativistic field theories

Recent work on purely transmitting ‘jump-defects’ in the sine-Gordon model and other relativistic field theories is extended to non-relativistic models. In all the cases investigated the defect

Hamiltonian methods in the theory of solitons

The Nonlinear Schrodinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples

Liouville integrable defects: the non-linear Schrödinger paradigm

A bstractA systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrödinger model in the presence of a single

Darboux Transformations and Solitons

In 1882 Darboux proposed a systematic algebraic approach to the solution of the linear Sturm-Liouville problem. In this book, the authors develop Darboux's idea to solve linear and nonlinear partial