In this paper, we construct the Lax pair for a soliton transmission system in nonuniform optical fibers and give N-soliton solution using the Darboux transformation. The explicit one-soliton and two-soliton solutions are presented. Further, we discuss the interaction scenario between two neighboring solitons and the effect of the inhomogeneities of the fiber (z0) on the interaction between two ...

In this paper, we derive a Bäcklund transformation for the supersymmetric Korteweg-de Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Korteweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 19...

The Bäcklund Transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite dimensional dynamical systems. It has recently been used to study the stability of these special solutions. We offer here a dynamical perspective on the Bäcklund Transform, prove an abstract orbital stability theorem, and dem...

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We specially discuss the soliton solutions of the K(m, n) equation and KdV-K(m, n) equation. Furthermore for the mixed models of linear and nonli...

A Darboux transformation for two new differential-integral equations in the Manakov hierarchy is given by using the gauge transformation between the corresponding matrix spectral problems. As an application of the Darboux transformation, soliton solutions of the two equations are obtained. 1. INTRODUCTION In the past few years, there are extensive development in the area of nonlinear mathematic...

We obtain an accurate estimate for the peak intensities of multi-soliton complexes for a Kerr-type nonlinearity in the (1+ 1) dimension problem. Using exact analytical solutions of the integrable set of nonlinear Schrödinger equations, we establish a rigorous relationship between the eigenvalues of incoherently-coupled fundamental solitons and the range of admissible intensities. A clear geomet...

The complex eikonal equation in (3+1) dimensions is investigated. It is shown that this equation generates many multi soliton configurations with arbitrary value of the Hopf index. In general, these eikonal hopfions do not have the toroidal symmetry. For example, a hopfion with topology of the trefoil knot is found. Moreover, we argue that such solitons might be helpful in construction of appro...

Keywords: (3 + 1)-dimensional Jimbo–Miwa equation Hirota bilinear form Wronskian determinant solution a b s t r a c t In this paper, we obtain two kinds of sufficient conditions consisting of systems of linear partial differential equations, which guarantee that the corresponding Wroskian determinant solves the (3 + 1)-dimensional Jimbo–Miwa equation in the Hirota bilinear form. Our results sug...