Related papers: A numerical direct scattering method for the perio…
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree…
Recently it was discussed the Inverse Scattering Method, Part I. (paper I.) . It was a methodological Part with an example - soliton (kink) solution of the Sine-Gordon Equation. The aim of the paper I. was to introduce the Inverse…
A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the temporal variable $t,$ and they are…
The aim of this paper is to introduce the Inverse Scattering Method for later studies of some problems in nonlinear dynamics, and describe the kink solution of the Sine Gordon Equation using the Inverse Scattering Method as a methodological…
The generalized sine-Gordon (sG) equation was derived as an integrable generalization of the sG equation. In this paper, we develop a direct method for solving the generalized sG equation without recourse to the inverse scattering method.…
We implement the numerical inverse scattering transform (NIST) for the sine-Gordon equation in laboratory coordinates on the real line using the method developed by Trogdon, Olver and Deconinck. The NIST allows one to compute the solution…
We address the scattering problem in two-dimensional integrable models, focusing on the sine-Gordon theory. We use the S-matrix bootstrap approach based on analytical properties of the S-matrix to compute scattering amplitudes of the…
A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators…
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the…
The inverse scattering theory for the sine-Gordon equation discretized in space and both in space and time is considered.
One of the difficulties associated with the scattering problems arising in connection with integrable systems is that they are frequently non-self-adjoint, making it difficult to determine where the spectrum lies. In this paper, we consider…
In this paper the quantum direct scattering problem is solved for the Sine-Gordon model. Correlators of the Jost functions are derived by the angular quantization method.
The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations. Notably, this method can be extended to fractional nonlinear evolution equations characterized by anomalous…
In this paper, we develop the dressing method to study the exact solutions for the vector sine-Gordon equation. The explicit formulas for one kink and one breather are derived. The method can be used to construct multi-soliton solutions.…
We present the study of the one-dimensional Klein-Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker $M_{\kappa,\mu}(x)$ function. The reflection and transmission coefficients are calculated in…
We develop the direct scattering theory for the KdV equation with step-like finite-gap backgrounds under perturbations. More precisely, we consider initial data that asymptotically approach two distinct one-gap periodic travelling wave…
We study scattering properties of topological solitons in two classes of models, which are generalizations of the Sine-Gordon model and which have recently been proposed by Bazeia et al. These two classes of models depend on an integer…
We construct various types of degenerate multi-soliton and multi-breather solutions for the sine-Gordon equation based on B\"{a}cklund transformations, Darboux-Crum transformations and Hirota's direct method. We compare the different…
The scattering problem for the Klein-Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein-Gordon equation we prove the existence of the scattering operator.
We study the 1D Klein-Gordon equation with variable coefficient cubic nonlinearity. This problem exhibits a striking resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…