Abstract
ABSTRACT In this work, we study the double chain Deoxyribonucleic acid (DNA) model, the study will be carried out by using two analytical methods, namely, Lie transformation method, then combined with the singular manifold method (SMM). Six cases are studied for different vector combinations. Two successive symmetry reductions transform the equation to an ordinary differential equation (ODE). We next apply the singular manifold method to the obtained ordinary differential equations. This will result in a Schwarzian derivative whose solution leads to soliton solutions for longitudinal and transversal motions. The solutions contain different types of wave solutions, N-solitons, kink and periodic wave solutions. Some of the resulting solutions are graphically illustrated.
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