modified Korteweg?de Vries equation
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1: 28.20 Definitions and Basic Properties
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§28.20(i) Modified Mathieu’s Equation
►When is replaced by , (28.2.1) becomes the modified Mathieu’s equation: ►
28.20.1
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§28.20(iv) Radial Mathieu Functions ,
… ►§28.20(vi) Wronskians
…2: 30.2 Differential Equations
§30.2 Differential Equations
►§30.2(i) Spheroidal Differential Equation
… ► … ►The Liouville normal form of equation (30.2.1) is … ►§30.2(iii) Special Cases
…3: 31.2 Differential Equations
§31.2 Differential Equations
►§31.2(i) Heun’s Equation
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31.2.1
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§31.2(v) Heun’s Equation Automorphisms
… ►Composite Transformations
…4: 29.2 Differential Equations
§29.2 Differential Equations
►§29.2(i) Lamé’s Equation
… ►§29.2(ii) Other Forms
… ►Equation (29.2.10) is a special case of Heun’s equation (31.2.1).5: 15.10 Hypergeometric Differential Equation
§15.10 Hypergeometric Differential Equation
►§15.10(i) Fundamental Solutions
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15.10.1
►This is the hypergeometric differential equation.
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6: 32.2 Differential Equations
§32.2 Differential Equations
►§32.2(i) Introduction
►The six Painlevé equations – are as follows: … ►§32.2(ii) Renormalizations
… ► …7: 28.2 Definitions and Basic Properties
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§28.2(i) Mathieu’s Equation
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28.2.1
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►This is the characteristic equation of Mathieu’s equation (28.2.1).
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§28.2(iv) Floquet Solutions
… ► …8: 32.13 Reductions of Partial Differential Equations
§32.13 Reductions of Partial Differential Equations
►§32.13(i) Korteweg–de Vries and Modified Korteweg–de Vries Equations
►The modified Korteweg–de Vries (mKdV) equation … ►The Korteweg–de Vries (KdV) equation … ►§32.13(iii) Boussinesq Equation
…9: 10.29 Recurrence Relations and Derivatives
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§10.29(i) Recurrence Relations
►With defined as in §10.25(ii), … ►For results on modified quotients of the form see Onoe (1955) and Onoe (1956). ►§10.29(ii) Derivatives
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10.29.5