New exact solutions for the nonlinear Schrödinger's equation with anti-cubic nonlinearity term via Lie group method

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Computer Science & Engineering Department

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Research Article

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The nonlinear Schrödinger's equation with anti-cubic nonlinearity was studied via the Lie group method. At first, we obtained the infinitesimal generators, Lie point symmetries and symmetry reduction by implementing the invariance criteria of the Lie group method on the nonlinear Schrödinger's equation with anti-cubic nonlinearity. After that, we used these symmetries for constructing the reduced ordinary differential equations. Corresponding to the reduced nonlinear ordinary differential equations, initially, the method of the general elliptic equations is described and is applied for constructing the exact travelling wave solutions. The basic idea is that the general elliptic equation containing five parameters. By specific choices of these parameters, we got sub-equations involving three parameters like the Riccati equation, generalized Riccati equation and the ordinary auxiliary equation. In contrast, we got sub-equations involving four parameters like an extended auxiliary function method with other choices. Consequently, many new families of rational formal solutions and other famous forms like bright solitons, singular solitons and dark –singular combo soliton are obtained. Finally, the differential transform (DTM) – Padé method is described and applied for constructing new solutions in closed form.

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