eng Science and Education Publishing Applied Mathematics and Physics 2333-4886 2017-06-24 5 3 77 84 10.12691/amp-5-3-1 AMP2017531 article Alphonse HOUWE ahouw220@yahoo.fr 1 2 YERIMA KLOFAI 3 Boudoue Hubert Malwe 3 Serge Y. Doka 3 4 Department of Marine engineering, Limbe Nautical Arts and Fisheries Institute, P.O. Box. 485 Limbe, Cameroon Department of Physics, Higher Teachers' Training College, University of Maroua, P.O. Box, 55, Maroua, Cameroon Exact traveling soliton solutions for the Josephson nonlinear Left-handed transmission line (NL-JLHTL) based on the periodic structure of an array of Josephson junctions (JJs) are investigated. The nonlinearity of the Josephson left-handed transmission line (JLHTL) is due to the highly nonlinear nature of the JJs that provide the shunt inductances required to realize an LHTL. Applying the generalized Ricati methods, we analytically and successfully derive exact traveling kink solitons, bright and dark solitary wave solutions on this network. The left-handedness of the line is explicitly confirmed in numerical simulations with the existence of bright and dark soliton solutions in good agreement with analytical predictions. http://pubs.sciepub.com/amp/5/3/1/amp-5-3-1.pdf Josephson nonlinear left-handed transmission line Josephson junction Envelope solitons and kink-soliton