Two different classes of Wronskian conditions to a \((3 + 1)\)-dimensional generalized shallow water equation (Q1757851)
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scientific article; zbMATH DE number 6102605
| Language | Label | Description | Also known as |
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| English | Two different classes of Wronskian conditions to a \((3 + 1)\)-dimensional generalized shallow water equation |
scientific article; zbMATH DE number 6102605 |
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Two different classes of Wronskian conditions to a \((3 + 1)\)-dimensional generalized shallow water equation (English)
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7 November 2012
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Summary: Based on the Hirota bilinear method and Wronskian technique, two different classes of sufficient conditions consisting of linear partial differential equation systems are presented, which guarantee that the Wronskian determinant is a solution to the corresponding Hirota bilinear equation of a \((3 + 1)\)-dimensional generalized shallow water equation. Our results show that the nonlinear equation possesses rich and diverse exact solutions such as rational solutions, solitons, negatons, and positons.
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Hirota bilinear method
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Wronskian technique
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linear partial differential equations
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generalized shallow water equation
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