Abstract
This paper comprises the extraction of many new general exact soliton solutions of the ill-posed Boussinesq equation, which has a number of applications in mathematical physics, by employing auxiliary equation method. The method successfully yields bell shape soliton, singular soliton, topological (dark) soliton, non-topological (bright) soliton and periodic soliton solutions of nonlinear partial differential equations solutions. These solutions are greater in number as compared to those attained by the exiting techniques. Parameters, contained in the solutions are given appropriate values for intelligible physical facets and vivid graphical view. Our results justify the efficacy, validity and favorability of auxiliary equation method for promising results while solving many other nonlinear partial differential equations.
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