A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the co...

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

In this note we show that the single soliton solutions known previously in the 1 + 1 dimensional affine Toda field theories from a variety of different methods [1, 2, 3, 4], are in fact not the most general single soliton solutions. We exhibit single soliton solutions with additional small parameters which reduce to the previously known solutions when these extra parameters are set to zero. The...

In this paper, we investigate analytically and numerically the modulational instability in a model of nonlinear physical systems like nonlinear periodic lattices. This model is described by the discrete complex cubic quintic Ginzburg-Landau equation with non-local quintic term. We produce characteristics of the modulational instability in the form of typical dependences of the instability growt...

In this paper, the topological (dark) as well as non-topological (bright) soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that, it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc...) envelope...

We announce a detailed investigation of limits of N-soliton solutions of the Korteweg-deVries (KdV) equation as N tends to infinity. Our main results provide new classes of KdV-solutions including in particular new types of soliton-like (reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one-dimensional Schrödinger operators and explicitly construct smooth and re...

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Bäcklund transformation, and the method of solving a Riccati map by exploiting two known particular solutions. This leads to an expression for the N -soliton-type solutions of a generic equation within this class. As a particu...

Soliton solutions of the one-dimensional (1D) complex Ginzburg-Landau equations (CGLE) are analyzed. %e have developed a simple approach that applies equally to both the cubic and the quintic CGLE. This approach allows us to find an extensive list of soliton solutions of the COLE, and to express all these solutions explicitly. In this way, we were able to classify them clearly. %'e have found a...

The interactions between soliton solutions of integrable models are usually considered to be completely elastic. That is to say, the amplitude, velocity and wave shape of solitons are not changed after nonlinear interaction [1]. However, for some specific solutions of some (2+1)-dimensional models, the interactions among solitonic excitations are not completely elastic since their shapes are ch...

We study the static Einstein equation coupled with a scalar field with axial symmetry. The zero curvature equation both for the scalar field and a part of the metric in the scalar-Einstein equation enables one to obtain soliton solutions for both the scalar field and the metric. Of the infinite series of solutions for the metric and the scalar field we focus on the solution composed of 4-solito...