Related papers: An Approximation Method for the Scattering Data of…
Interpretation of random wave field on a shallow water in terms of Fourier spectra is not adequate, when wave amplitudes are not infinitesimally small. A nonlinearity of wave fields leads to the harmonic interactions and random variation of…
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…
We present a robust approach to incorporating models for the time-variable broadening of the pulse profile due to scattering in the ionized interstellar medium into profile-domain pulsar timing analysis. We use this approach to…
We address the nonlinear Schrodinger equation with intensity-dependent dispersion which was recently proposed in the context of nonlinear optical systems. Contrary to the previous findings, we prove that no solitary wave solutions exist if…
We model discrete spatial solitons in a periodic nonlinear medium encompassing any degree of transverse non locality. Making a convenient reference to a widely used material -nematic liquid crystals-, we derive a new form of the discrete…
The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The…
We develop a general analytical framework for determining the probability distribution of random nonlinear wave fields governed by the focusing nonlinear Schr\"odinger equation (fNLSE) in regimes where typical realizations are dominated by…
Matter-wave bright solitons are predicted to reflect from a purely attractive potential well although they are macroscopic objects with classical particle-like properties. The non-classical reflection occurs at small velocities and a…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
Dynamics of solitons is considered in the framework of an extended nonlinear Schrodinger equation (NLSE), which is derived from a system of the Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves. The…
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that…
We study the amplitude dynamics of two-dimensional (2D) solitons in a fast collision described by the coupled nonlinear Schr\"odinger equations with a saturable nonlinearity and weak nonlinear loss. We extend the perturbative technique for…
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amplitudes of three resonant wave modes. Collisions of wave…
We construct a perturbative framework for understanding the collision of solitons (more precisely, solitary waves) in relativistic scalar field theories. Our perturbative framework is based on the suppression of the space-time interaction…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
We show that the initial-value problem for the Benjamin-Ono equation on $\mathbb{R}$ with $L^2(\mathbb{R})$ rational initial data with only simple poles can be solved in closed form via a determinant formula involving contour integrals. The…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…