: Optical separate spatial dark and bright soliton pairs in steady-state case in one dimension, for a series circuit consisting of two-photon photorefractive (PR) crystal are investigated. Each crystal can be supported the spatial soliton, and at least one must be photovoltaic. The two solitons are known collectively as separate spatial soliton pairs with dark–dark, bright–dark and bright–brigh...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N = 1 supersymmetric Hirota operators. Using them, we bilinearize SUSY nonlinear evolution equations. The super-soliton solutions and extension to SUSY sine-Gordon are also discussed. As a quite strange paradox it is shown that the Lax integrable SUSY KdV of Manin-Ra...

In this paper we investigate the existence of soliton solutions for a modified form of the Zakharov equations describing modulational instabilities in quantum plasmas. In particular, we show that quantum effects suppress the easily identifiable soliton solutions, obtained in the adiabatic limit. In this limit, the quantum Zakharov equations become a coupled fourth order system, not amenable to ...

For n+1 ≥ 3, we construct complete solutions to Ricci flow on R which encounter global singularities at a finite time T . The singularities are forming arbitrarily slowly with the curvature blowing up arbitrarily fast at the rate (T − t)−2λ for λ ≥ 1. Near the origin, blow-ups of such a solution converge uniformly to the Bryant soliton. Near spatial infinity, blow-ups of such a solution converg...

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...

We consider the generalized Korteweg-de Vries equation ∂tu + ∂ 3 xu + ∂x(u ) = 0, (t, x) ∈ R2, in the supercritical case p > 5, and we are interested in solutions which converge to a soliton in large time in H. In the subcritical case (p < 5), such solutions are forced to be exactly solitons by variational characterization [1, 19], but no such result exists in the supercritical case. In this pa...

We speculate that the universe is filled with stars composed of electromagnetic and dilaton fields. We calculate soliton-like solutions of these fields and show that their energy can be converted into a relativistic plasma in an explosive way whioch produces strong gamma-ray bursts observed in the universe. The conversion proceeds as in classical detonation theory by a relativistic self-similar...

Using a generalized transfer matrix method we exactly solve the Schrödinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating soliton-like wave packet and the wave front is wedge shaped. In a statistical mechanics framework our solution represents the partition sum of a directed polymer s...

The interaction and propagation of optical pulses in a nonlinear waveguide array is described by the discrete nonlinear Schrödinger equation i∂zψn = −D(ψn+1 + ψn−1 − 2ψn) − γ|ψn|ψn, (1) whereD is a dispersion (or diffraction) coefficient, and γ is a measure of the nonlinearity. By means of the variational approximation, we study the discrete soliton solutions of this equation. We use a trial fu...

It is proven that there are precisely n odd-parity sphaleron-like unstable modes of the n-th Bartnik-McKinnon soliton and the n-th non-abelian black hole solution of the Einstein-Yang-Mills theory for the gauge group SU(2). On leave from Physical–Technical Institute of the Academy of Sciences of Russia, Kazan 420029, Russia On leave of absence from Tbilisi Mathematical Institute, 380093 Tbilisi...