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Korteweg–de Vries equation


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1: 32.13 Reductions of Partial Differential Equations
§32.13(i) Kortewegde Vries and Modified Kortewegde Vries Equations
The modified Kortewegde Vries (mKdV) equationThe Kortewegde Vries (KdV) equation
2: 29.19 Physical Applications
§29.19(ii) Lamé Polynomials
Ward (1987) computes finite-gap potentials associated with the periodic Kortewegde Vries equation. …
3: 21.9 Integrable Equations
Typical examples of such equations are the Kortewegde Vries equation
4: 9.16 Physical Applications
An application of Airy functions to the solution of this equation is given in Gramtcheff (1981). … These first appeared in connection with the equation governing the evolution of long shallow water waves of permanent form, generally called solitons, and are predicted by the Kortewegde Vries (KdV) equation (a third-order nonlinear partial differential equation). …
5: 23.21 Physical Applications
§23.21(ii) Nonlinear Evolution Equations
For applications to soliton solutions of the Kortewegde Vries (KdV) equation see McKean and Moll (1999, p. 91), Deconinck and Segur (2000), and Walker (1996, §8.1). …
6: 22.19 Physical Applications
§22.19(iii) Nonlinear ODEs and PDEs
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 Kortewegde 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. …
7: Bibliography R
  • R. R. Rosales (1978) The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendent. Proc. Roy. Soc. London Ser. A 361, pp. 265–275.
  • 8: Bibliography H
  • S. P. Hastings and J. B. McLeod (1980) A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.
  • 9: Bibliography K
  • M. D. Kruskal (1974) The Korteweg-de Vries Equation and Related Evolution Equations. In Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972), A. C. Newell (Ed.), Lectures in Appl. Math., Vol. 15, pp. 61–83.
  • 10: Bibliography D
  • B. Deconinck and H. Segur (2000) Pole dynamics for elliptic solutions of the Korteweg-de Vries equation. Math. Phys. Anal. Geom. 3 (1), pp. 49–74.