KdV%20equation
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11: 22.19 Physical Applications
§22.19(iii) Nonlinear ODEs and PDEs
►Many nonlinear ordinary and partial differential equations have solutions that may be expressed in terms of Jacobian elliptic functions. These include the time dependent, and time independent, nonlinear Schrödinger equations (NLSE) (Drazin and Johnson (1993, Chapter 2), Ablowitz and Clarkson (1991, pp. 42, 99)), the Korteweg–de Vries (KdV) equation (Kruskal (1974), Li and Olver (2000)), the sine-Gordon equation, and others; see Drazin and Johnson (1993, Chapter 2) for an overview. … …12: 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
…13: 20 Theta Functions
Chapter 20 Theta Functions
…14: 28.16 Asymptotic Expansions for Large
15: 10.73 Physical Applications
§10.73(ii) Spherical Bessel Functions
…16: Bibliography O
17: Bibliography N
18: 3.8 Nonlinear Equations
19: 28.18 Integrals and Integral Equations
§28.18 Integrals and Integral Equations
…20: 28.35 Tables
§28.35 Tables
… ►Ince (1932) includes eigenvalues , , and Fourier coefficients for or , ; 7D. Also , for , , corresponding to the eigenvalues in the tables; 5D. Notation: , .
Kirkpatrick (1960) contains tables of the modified functions , for , , ; 4D or 5D.
National Bureau of Standards (1967) includes the eigenvalues , for with , and with ; Fourier coefficients for and for , , respectively, and various values of in the interval ; joining factors , for with (but in a different notation). Also, eigenvalues for large values of . Precision is generally 8D.
Zhang and Jin (1996, pp. 521–532) includes the eigenvalues , for , ; (’s) or 19 (’s), . Fourier coefficients for , , . Mathieu functions , , and their first -derivatives for , . Modified Mathieu functions , , and their first -derivatives for , , . Precision is mostly 9S.