on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...

In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories [1] [2] or the skyrme model of hadrons have been proposed as possible non-perturbative bound states which remain stable due to topological quantum numbers. Furthermore whe...

The soliton dressing matrices for the higher-order zeros of the RiemannHilbert problem for theN -wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric multiplicity is 1, the general soliton dressing matrix is derived. The theory is applied to the study of higher-order soliton solutions in the three-wave interaction mod...

This paper, deals with the (2+1)-dimensional complex three coupled nonlinear Maccari’s model (3-CCME) by utilizing recently presented modified new Kudryashov method (mNKM). The focus of this article is to obtain non-topological soliton solution 3-CCME applying mKNM method, which has not been applied before investigated problem. Applying proposed successfully, besides problem, breather-like type...

An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schrödinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new types...

We discuss the formation of nontopological solitons in a second-order phase transition in the early Universe. Ratios of dimensionless coupling constants in the Lagrangian determine their abundance and mass. For a large range of parameters, non-topological solitons can be cosmologically significant, contributing a significant fraction of the present mass density of the Universe. Submitted to Phy...

In the process of searching for explicit solutions, quite a few systematic methods have been developed, such as inverse scattering transformation [1], Darboux transformations [2], Hirota’s bilinear method [3-5], and so on. Among them, the bilinear method first proposed by Hirota provides us with a comprehensive approach to construct exact solutions of nonlinear evolution equations (NEEs). Meanw...

We address some aspects of four-dimensional chiral N = 1 supersymmetric theories on which the scalar manifold is described by Kähler geometry and can further be viewed as Kähler–Ricci soliton generating a one-parameter family of Kähler geometries. All couplings and solutions, namely the BPS domain walls and their supersymmetric Lorentz invariant vacua turn out to be evolved with respect to the ...