Abstract
In the present work, the new exact solutions of the Boiti—Leon—Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti—Leon—Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differential equations with one variable less at each step and eventually to a system of ordinary differential equations (ODEs). Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.
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