As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

The paper investigates solutions and Lax pairs through bilinear Backlund transformations for some supersymmetric equations. We derive variety of from the known transformations. Besides, using gauge invariance (super) Hirota derivatives we may get deformed consequently with fermionic parameters. Examples are KdV equation KdV1 equation.

We introduce certain Backlund transformations for rational solutions of the Painleve VI equation. These act on a family tau functions. They are obtained from reducing Hirota bilinear equations that describe relation between points in 3 component polynomial KP Grassmannian. In this way we obtain root lattice A5. also show A5 can be related to F4(1) lattice. thus relate functions, parametrized by...

The construction of generalized Backlund transformation for the $A_n$ Affine Toda hierarchy is proposed in terms gauge acting on zero curvature representation. Such based upon graded structure underlying affine algebra which induces a classification transformations. Moreover, explicit examples $su(3)$ and $su(4)$ lead to uncover interesting composition properties various types universality char...

1. The investigation of nonlinear evolution equations in multi-dimensional space-time has received much interest recently [ 1-7] . Although a lot of progress has been made in extending the inverse-scattering transform to higher-dimensional equations,such as the Kadomtsev-Petviashvili (KP) equation [1 ], some of the essential features are not completely understood. In order to obtain more insigh...