We study in a systematic way all static solutions of the Goldstone model in 1+1 dimension with a periodicity condition imposed on the spatial coordinate. The solutions are presented in terms of the standard trigonometric functions and of Jacobi elliptic functions. Their stability analysis is carried out, and the complete list of classically stable quasi-topological solitons is given.

The Mel’nikov equation is a (2+1) dimensional nonlinear evolution equation admitting boomeron type solutions. In this paper, after showing that it satisfies the Painlevé property, we obtain exponentially localized dromion type solutions from the bilinearized version which have not been reported so far. We also obtain more general dromion type solutions with spatially varying amplitude as well a...

we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota's bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...

In this paper we study the noncommutative extension of a modified U(n) sigma model in 2 + 1 dimensions. Using the method of dressing transformations, an iterative approach for the construction of solutions from a given seed solution, we demonstrate the construction of multi-soliton and soliton-antisoliton configurations for general n. As illustrative examples we discuss U(3) solitons and consid...

The existence of a faster-than-light particle is in direct opposition to Einstein's relativity and the principle causality. However, we show that theory classical relativistic fields not inherently inconsistent with particle-like soliton solutions $1+1$ dimensions. We introduce two extended KG models ($k$-fields) lead zero-energy nonzero-energy stable solution faster-than light speeds, respecti...

parameterized by θ ∈ R . But we do not expect that the “sum” of two such solutions will again be a solution. However, the special class of soliton equations, the subject of this article, does have a form of nonlinear superposition. An n-soliton solution is a solution that is asymptotic to a nontrivial sum of n solitary waves ∑n i=1 fi(x− cit) as t → −∞ and to the sum of the same waves ∑n i=1 fi...

We construct N-soliton solutions to the equation called Q3 in the recent Adler-Bobenko-Suris classification. An essential ingredient in the construction is the relationship of (Q3) δ=0 to the equation proposed by Nijhoff, Quispel and Capel in 1983 (the NQC equation). This latter equation has two extra parameters, and depending on their sign choices we get a 4-to-1 relationship from NQC to (Q3) ...

The paper deals with constructing an asymptotic one-phase soliton-like solution to the Benjamin–Bona–Mahony equation variable coefficients and a strong singularity making use of non-linear WKB technique. influence small-parameter value on structure qualitative properties solution, as well accuracy which satisfies considerable equation, have been analyzed. It was demonstrated that due singularit...

The inverse scattering problem method application to construction of exact solution for Maxwell dilaton gravity system ia considered. By use of Belinsky and Zakharov L A pair the solution of the theory is constructed. The rotating Kerr like configuration with NUT parameter is obtained.

We describe the interaction pattern in the x–y plane for a family of soliton solutions of the Kadomtsev–Petviashvili (KP) equation, (−4ut + uxxx + 6uux)x + 3uyy = 0. The solutions considered also satisfy the finite Toda lattice hierarchy. We determine completely their asymptotic patterns for y → ±∞, and we show that all the solutions (except the 1-soliton solution) are of resonant type, consist...