Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are discovered and the structure of the induced space-time geometry is discussed. These solutions have interesting features and may serve as a starting point for fur...

In this paper many soliton-like solutions with the arbitrary functions of y and t are obtained for the 1+2D Calogero-Bogoyavlenskii-Schif equation by means of some generalized ansatz and symbolic computation. Some new exact solutions are also presented from the obtained soliton-like solutions. Shock wave solution is only a special case.

Based on the factorization of soliton equations into two commuting integrable xand t-constrained flows, we derive N -soliton solutions for mKdV equation via its xand t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.

We report an exact bright and dark soliton solution to the nonlinear evolution equation derived by MOSES and WISE (Phys. Rev. Lett. 97, 2006, 073903) for cascaded quadratic media beyond the slowly varying envelope approximations. The integrability aspects of the model are addressed. The travelling wave hypothesis as well as the ansatz method are employed to obtain an exact 1-soliton solution. B...

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...

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...

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...

In the previous papers (notably, Y. Kodama, J. Phys. A 37, 11169-11190 (2004), and G. Biondini and S. Chakravarty, J. Math. Phys. 47 033514 (2006)), we found a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation. The line-soliton solutions are solitary waves which decay exponentially in (x,y)-plane except along certain rays. In this paper, we show that those...