The algebraic geometric approach to N -component systems of nonlinear integrable PDE’s is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical pheno...

In this paper, the direct Ansäz method is used for constructing the multi-wave solutions to the (2+1)-dimensional extension of the Korteweg de-Vries (shortly EKdV) equation. A new breather type of three-wave solutions including periodic breather type soliton solution, breather type of two-solitary solution are obtained. Some cases with specific values of the involved parameters are plotted for ...

We present new solutions in terms of elementary functions of the multi-component nonlinear Schrödinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. ...

The main purpose of this paper is to give a survey of recent development on a classification of soliton solutions of the KP equation. The paper is self-contained, and we give a complete proof for the theorems needed for the classification. The classification is based on the Schubert decomposition of the real Grassmann manifold, Gr(N, M), the set of N -dimensional subspaces in RM . Each soliton ...

The Painlevé integrability of the 2+1 dimensional AKNS system is proved. Using the standard truncated Painlevé expansion which corresponds to a special Bäcklund transformation, some special types of the localized excitations like the solitoff solutions, multi-dromion solutions and multi-ring soliton solutions are obtained. PACS. 02.30.Ik Integrable systems – 02.30.Jr Partial differential equati...

The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N -soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial...

To find nontrivial high dimensional integrable models (especially in (3+l)-dimensions) is one of the most important problems in nonlinear physics. A systematic method to find some nontrivial high dimensional integrable models is established by means of noninvertible deformation relations. Starting f rom a noninvertible Miura type transformation, we find that the (l + l)-dimensional sinhGordon m...

The analytical solutions for a (2+1)-dimensional breaking solution equation is proposed in this paper by using mapping and projective method darboux transformation, and Some exact propagating solutions are constructed for this Breaking equation, and the M × N multi-soliton could be obtained by using Weierstrassp function and setting the perfect parameters. The potential application of breaking ...