nonlinear evolution equations

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1: Peter A. Clarkson

… ►His well-known book Solitons, Nonlinear Evolution Equations and Inverse Scattering (with M. …

2: 23.21 Physical Applications

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§23.21(ii) Nonlinear Evolution Equations

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3: 29.19 Physical Applications

… ►Clarkson (1991) solves nonlinear evolution equations. …

4: Mark J. Ablowitz

… ►Some of the relationships between IST and Painlevé equations are discussed in two books: Solitons and the Inverse Scattering Transform and Solitons, Nonlinear Evolution Equations and Inverse Scattering. …

5: Bibliography

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Solitons, Nonlinear Evolution Equations and Inverse Scattering. London Mathematical Society Lecture Note Series, Vol. 149, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-38730-2, Document, Link, MathReview (Walter Oevel), ZentralBlatt

Referenced by:

§22.19(ii), §22.19(iii), §32.11(ii), §32.5, §9.16, Profile Mark J. Ablowitz, Profile Peter A. Clarkson.

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6: Bibliography C

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Nonclassical Symmetry Reductions and Exact Solutions for Physically Significant Nonlinear Evolution Equations. In Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (Edmonton, AB, 1990), W. Rozmus and J. A. Tuszynski (Eds.), pp. 72–79.

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External Links:

MathReview

Referenced by:

§29.19(ii).

Encodings:

BibTeX

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7: Bibliography S

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Asymptotic solutions of nonlinear evolution equations and a Painlevé transcendent. Phys. D 3 (1-2), pp. 165–184.

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External Links:

Document, ZentralBlatt

Referenced by:

§32.11(ii).

Encodings:

BibTeX

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8: Bibliography K

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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.

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External Links:

MathReview (G. L. Lamb, Jr.), ZentralBlatt

Referenced by:

§22.19(iii).

Encodings:

BibTeX

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9: 9.16 Physical Applications

… ►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 Korteweg–de Vries (KdV) equation (a third-order nonlinear partial differential equation). …

10: 22.19 Physical Applications

… ►The subsequent time evolution is always oscillatory with period $4K\left(k\right)/\sqrt{1+2\eta }$ and modulus $k=1/\sqrt{2+{\eta }^{-1}}$: … ►

§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. … …