An optimal system of group-invariant solutions and conserved quantities of a nonlinear fifth-order integrable equation
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Abstract In this work, we perform Lie group analysis on a fifth-order integrable nonlinear partial differential equation, which was recently introduced in the literature and contains two dispersive terms. We determine a one-parameter group of transformations, an optimal system of group invariant solutions, and derive the corresponding analytic solutions. Topological kink, periodic and power series solutions are obtained. The existence of a variational principle for the underlying equation is proven using Helmholtz conditions and, thereafter, both local and nonlocal conserved quantities are obtained by utilising Noether’s theorem and a homotopy integral approach.
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2004 ◽
Vol 9
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pp. 93-104
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2020 ◽
Vol 43
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pp. 8823-8840
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2015 ◽
Vol 56
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pp. 053504
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2018 ◽
Vol 3
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pp. 409-418
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2018 ◽
Vol 69
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pp. 14
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