In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1) -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applicat...

in this paper, the exp-function method, with the aid of a symbolic computation system such as maple, is applied to the (2+1) -dimensional calogero bogoyavlanskii schiff equation. exact and explicit generalized solitary solutions are obtained in more general forms. the free parameters can be determined by initial or boundary conditions. the method is straightforward and concise, and its applicat...

In this work, we develop two new (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation and negative-order KdV-CBS (nKdV-nCBS) equation. The newly developed equations pass the Painlevé integrability test via examining compatibility conditions for each model. We examine dispersion relation derive multiple soliton solutions

We find two one-parametric families of recursion operators and use them to construct higher symmetries for the Calogero--Bogoyavlenskii--Schiff breaking soliton equation. Then we prove that from first family pair-wise commute with respect Nijenhuis bracket (are compatible).

In this work, the generalized (2+1) and (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equations are studied. We employ the Cole-Hopf transformation and the Hirota bilinear method to derive multiple-soliton solutions and multiple singular soliton solutions for these equations. The necessary conditions for complete integrability of each equation are derived.

The general KdV equation (gKdV) derived by T. Chou is one of the famous (1 + 1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. In this paper a higher-dimensional gKdV equation, which is integrable in the sense of the Painlevé test, is presented. A transformation that links this equation to the canonical form of the Calogero–Bogoy...

We present two hierarchies of partial differential equations in $2+1$ dimensions. Since there exist reciprocal transformations that connect these to the Calogero-Bogoyavlenski-Schiff equation and its modified version, we can prove one be considered as a version other. The connection between them achieved by means combination Miura transformations.

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota’s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented. Keywords—EHTA, (2+1)-dimensional CBS equat...