Related papers: Are Simple Real Pole Solutions Physical?
A naked singularity is formed by the collapse of a Sine-Gordon soliton in 1+1 dimensional dilaton gravity with a negative cosmological constant. We examine the quantum stress tensor resulting from the formation of the singularity.…
A solution of the 6D gravitational model, which has the pole configuration, is found. The vacuum setting is done by the 6D Higgs potential and the solution is for a family of the vacuum and boundary parameters. The boundary condition is…
We consider the critical focusing wave equation $(-\partial_t^2+\Delta)u+u^5=0$ in $\R^{1+3}$ and prove the existence of energy class solutions which are of the form [u(t,x)=t^\frac{\mu}{2}W(t^\mu x)+\eta(t,x)] in the forward lightcone…
The soliton resolution conjecture is one of the most interesting open problems in the theory of nonlinear dispersive equations. Roughly speaking it asserts that a solution with generic initial condition converges to a finite number of…
For a singular Liouville equation, it is plausible that a non-simple blowup phenomenon occurs around a quantized singular pole. The presence of complex blowup profiles of bubbling solutions presents substantial challenges in applications.…
It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these…
It is known that any {\em real coordinate transformation} (RCT) to compress waves in an unbounded domain into a bounded domain results in infinite oscillations that cannot be resolved by any grid-based method. In this paper, we intend to…
Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid…
A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density…
We take a soliton solution of a classical non-linear integrable equation and quench (suddenly change) its non-linearity parameter. For that we multiply the amplitude or the width of a soliton by a numerical factor $\eta$ and take the…
We consider the inverse scattering transform for the nonlinear Schr\"{o}dinger equation in laboratory coordinates (NLSLab equation) with nonzero boundary conditions (NZBCs) at infinity. In order to better deal with the scattering problem of…
The concept of soliton gas was introduced in 1971 by V. Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted soliton gas,…
The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon…
We consider soliton creation when there are "twist" degrees of freedom present in the model in addition to those that make up the soliton. Specifically we consider a deformed O(3) sigma model in 1+1 dimensions, which reduces to the…
The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz hypersurface. They…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
The current work investigates the soliton solutions of the Kaup-Boussinesq equation using the Inverse Scattering Transform method. We outline the construction of the Riemann-Hilbert problem for a pair energy-dependent spectral problems for…
A brief description of the novel approach towards solving few-body scattering problems in a finite-dimensional functional space of the $L_2$-type is presented. The method is based on the complete few-body continuum discretization in the…
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…
Molecular dynamics in pure water and aqueous salt solutions remain incompletely understood, partly due to the apparent contradictions between results from different spectroscopic techniques. In this work, we demonstrate, by detailed…