About the Project

Korteweg%E2%80%93de%20Vries%20equation

AdvancedHelp

(0.004 seconds)

1—10 of 536 matching pages

1: 32.13 Reductions of Partial Differential Equations
§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
§32.13(iii) Boussinesq Equation
2: 29.19 Physical Applications
§29.19(ii) Lamé Polynomials
Ward (1987) computes finite-gap potentials associated with the periodic Kortewegde Vries equation. …Hargrave (1978) studies high frequency solutions of the delta wing equation. …Roper (1951) solves the linearized supersonic flow equations. Clarkson (1991) solves nonlinear evolution equations. …
3: Tom H. Koornwinder
… …  1943 in Rotterdam, The Netherlands) is Professor Emeritus in the Kortewegde Vries Institute for Mathematics at the University of Amsterdam, The Netherlands. …
4: 18 Orthogonal Polynomials
… …
5: Bibliography D
  • C. de la Vallée Poussin (1896b) Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire M x + N . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
  • 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.
  • K. Dilcher (1987b) Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters. J. Number Theory 25 (1), pp. 72–80.
  • B. A. Dubrovin (1981) Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
  • T. M. Dunster (1997) Error analysis in a uniform asymptotic expansion for the generalised exponential integral. J. Comput. Appl. Math. 80 (1), pp. 127–161.
  • 6: 9.16 Physical Applications
    Details of the Airy theory are given in van de Hulst (1957) in the chapter on the optics of a raindrop. … In the study of the stability of a two-dimensional viscous fluid, the flow is governed by the Orr–Sommerfeld equation (a fourth-order differential equation). …An application of Airy functions to the solution of this equation is given in Gramtcheff (1981). Airy functions play a prominent role in problems defined by nonlinear wave equations. 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). …
    7: 21.9 Integrable Equations
    §21.9 Integrable Equations
    Typical examples of such equations are the Kortewegde Vries equation …and the nonlinear Schrödinger equations
    8: Bibliography
  • H. Airault, H. P. McKean, and J. Moser (1977) Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem. Comm. Pure Appl. Math. 30 (1), pp. 95–148.
  • D. E. Amos, S. L. Daniel, and M. K. Weston (1977) Algorithm 511: CDC 6600 subroutines IBESS and JBESS for Bessel functions I ν ( x ) and J ν ( x ) , x 0 , ν 0 . ACM Trans. Math. Software 3 (1), pp. 93–95.
  • D. E. Amos (1990) Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument. ACM Trans. Math. Software 16 (2), pp. 178–182.
  • G. E. Andrews, R. Askey, and R. Roy (1999) Special Functions. Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge.
  • M. J. Atia, A. Martínez-Finkelshtein, P. Martínez-González, and F. Thabet (2014) Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters. J. Math. Anal. Appl. 416 (1), pp. 52–80.
  • 9: Bibliography K
  • K. W. J. Kadell (1994) A proof of the q -Macdonald-Morris conjecture for B C n . Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
  • E. H. Kaufman and T. D. Lenker (1986) Linear convergence and the bisection algorithm. Amer. Math. Monthly 93 (1), pp. 48–51.
  • A. V. Kitaev and A. H. Vartanian (2004) Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.
  • C. Krattenthaler (1993) HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively q -binomial sums and basic hypergeometric series. Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
  • 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 H
  • P. I. Hadži (1973) The Laplace transform for expressions that contain a probability function. Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).
  • P. I. Hadži (1976a) Expansions for the probability function in series of Čebyšev polynomials and Bessel functions. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
  • P. I. Hadži (1976b) Integrals that contain a probability function of complicated arguments. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 80–84, 96 (Russian).
  • P. I. Hadži (1978) Sums with cylindrical functions that reduce to the probability function and to related functions. Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).
  • 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.