In this thesis, we discuss a class of physically important soliton equation―(2+1)-Dimensional Breaking Soliton Equationwhere by Hirota bilinear form method, extended homoclinic test technique, Lie symmetry methodand fractional extension of two-soliton Ansatz method, Breather wave solution, two-soliton solution, novel non-traveling wave solution for (2+1)-Dimensional Breaking SolitonEquation are obtained.
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