Geodesic
Solvable Nonlinear Evolution PDEs in Multidimensional Space
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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A class of solvable (systems of) nonlinear evolution PDEs in multidimensional space is discussed. We focus on a rotation-invariant system of PDEs of Schrödinger type and on a relativistically-invariant system of PDEs of Klein–Gordon type. Isochronous variants of these evolution PDEs are also considered.
Keywords: nonlinear evolution PDEs in multidimensions; solvable PDEs; NLS-like equations; nonlinear Klein–Gordon-like equations; isochronicity. 
@article{SIGMA_2006_2_a87,
     author = {Francesco Calogero and Matteo Sommacal},
     title = {Solvable {Nonlinear} {Evolution} {PDEs} in {Multidimensional} {Space}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2006},
     volume = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a87/}
}
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Francesco Calogero; Matteo Sommacal. Solvable Nonlinear Evolution PDEs in Multidimensional Space. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a87/

[1] Calogero F., “Motion of poles and zeros of special solutions of nonlinear and linear partial differential equations, and related “solvable” many body problems”, Nuovo Cimento B, 43 (1978), 177–241 | DOI | MR

[2] Calogero F., “A class of $C$-integrable PDEs in multidimensions”, Inverse Problems, 10 (1994), 1231–1234 | DOI | MR | Zbl

[3] Calogero F., Classical many-body problems amenable to exact treatments, Lecture Notes in Physics Monograph, 66, Springer-Verlag, Berlin–Heidelberg, 2001 | MR | Zbl

[4] Calogero F., Isochronous systems, Oxford University Press, Oxford, 2008, 250 pp. | MR | Zbl

[5] Erdélyi A. (ed.), Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953

[6] Gómez-Ullate D., Sommacal M., “Periods of the goldfish many-body problem”, J. Nonlinear Math. Phys., 12, suppl. 1 (2005), 351–362 | DOI | MR

[7] Mariani M., Calogero F., “Isochronous PDEs”, Theor. Math. Phys., 68 (2005), 958–968 | MR