Exact solution to higher-order nonlinear equations through gauge transformation (Q1088515)
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scientific article; zbMATH DE number 3991069
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Exact solution to higher-order nonlinear equations through gauge transformation |
scientific article; zbMATH DE number 3991069 |
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Exact solution to higher-order nonlinear equations through gauge transformation (English)
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1987
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A highly nonlinear hydrodynamic equation proposed by \textit{R. S. Johnson} [Proc. R. Soc. Lond., Ser. A 357, 131-141 (1977; Zbl 0375.76017)] is solved exactly, by gauge transforming (GT) it to the mixed nonlinear Schrödinger equation. The GT is generalized further, to generate a hierarchy of integrable higher-order nonlinear systems including some known equations, along with their Lax pairs, infinite sets of conserved quantities and exact solutions.
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Stokes instability
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highly nonlinear hydrodynamic equation
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gauge transforming
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mixed nonlinear Schrödinger equation
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hierarchy of integrable higher-order nonlinear systems
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Lax pairs
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infinite sets of conserved quantities
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exact solutions
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