Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation
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In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.
2021 ◽
pp. 100134
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2021 ◽
Vol 3
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pp. 100026
2007 ◽
Vol 32
(2)
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pp. 538-546
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2009 ◽
Vol 26
(5)
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pp. 054701
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2010 ◽
Vol 369
(1)
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pp. 133-143
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2019 ◽
Vol 78
(3)
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pp. 857-877
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