The integrability of the coupled Ramani equation with binary Bell polynomials

Binary Bell polynomial approach is applied to study the coupled Ramani equation, which is the generalization of the Ramani equation. Based on the concept of scale invariance, the coupled Ramani equation is written in terms of binary Bell polynomials of two dimensionless field variables, which leads to the bilinear coupled Ramani equation directly. As a consequence, the bilinear Bäcklund transformation, Lax pair and conservation laws are systematically constructed by virtue of binary Bell polynomials.

Soliton Solutions, Bäcklund Transformation and Lax Pair for Coupled Burgers System via Bell Polynomials

In this work, we apply the binary Bell polynomial approach to coupled Burgers system. In other words, we investigate possible integrability of referred system. Bilinear form and soliton solutions are obtained, some figures related to these solutions are given. We also get Bäcklund transformations in both binary Bell polynomial form and bilinear form. Based on the Bäcklund transformation, Lax pair is obtained. Namely, this is a study in which integrabilitiy of coupled burgers system is investigated.