The dynamics of dissipative matter wave bright solitons with three- body recombination and external feeding, in a highly asymmetric trap and a deformable shape optical lattice, is studied. Using the variational approach, we derive and analyze the variational equations for the time evolution of the width and amplitude of dissipative solitons, and effective potential of the system. We examine the effects of the optical lattice deformability on the stability of the system. Furthermore, we perform direct numerical experiments to confirm our analytical approach, and good agreement is observed.

Bose-Einstein condensates, bright solitons, variable shape potential, three-body recombination, external feeding.