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The stationary bright solitons that appear in the ground state of thespin-orbit coupled Bose-Einstein condensate (SOC-BEC) exhibit nodes. Weconsider SOC-BEC in combined linear and nonlinear optical lattices and studytheir effects on the matter-wave bright soliton and find that the parameters ofthe nonlinear lattice or atomic scattering length can be judiciouslymanipulated to have useful control over the nodes of the soliton. It is seenthat the soliton with large number of nodes is less stable compared to onehaving fewer number of nodes. We infer that that the synthetic spin-orbitcoupling induces instability in the ordinary matter-wave soliton.

Effects of optical lattices on bright solitons in spin-orbit coupled Bose-Einstein condensates