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Preface: Mark J. Ablowitz, Nonlinear waves and integrable systems. I. (English) Zbl 1347.35005

From the text: This special issue of Studies in Applied Mathematics and the following one are dedicated to Prof. Mark J. Ablowitz on the occasion of his seventieth birthday.

MSC:

35-03 History of partial differential equations
37-03 History of dynamical systems and ergodic theory
78-03 History of optics and electromagnetic theory
01A60 History of mathematics in the 20th century
01A61 History of mathematics in the 21st century
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
78A60 Lasers, masers, optical bistability, nonlinear optics
01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Ablowitz, Mark J.
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References:

[1] Ablowitz, The evolution of multiphase modes for nonlinear dispersive waves, Stud. Appl. Math 49 pp 225– (1970) · Zbl 0203.41001
[2] Ablowitz, Method for solving the Sine-Gordon equation, Phys. Rev. Lett 30 pp 1262– (1973)
[3] Ablowitz, Nonlinear evolution equations of physical significance, Phys. Rev. Lett 31 pp 125– (1973) · Zbl 1243.35143
[4] Ablowitz, Inverse scattering transform - Fourier analysis for nonlinear problems, Stud. Appl. Math 53 pp 249– (1974) · Zbl 0408.35068
[5] Ablowitz, Nonlinear differential-difference equations and Fourier analysis, J. Math. Phys 17 pp 1011– (1976) · Zbl 0322.42014
[6] Ablowitz, Nonlinear difference scheme and inverse scattering, Stud. Appl. Math 55 pp 213– (1976) · Zbl 0338.35002
[7] Ablowitz, Asymptotic solutions of Korteweg-deVries equation, Stud. Appl. Math 57 pp 13– (1977) · Zbl 0369.35055
[8] Ablowitz, Exact linearization of a Painlevé transcendent, Phys. Rev. Lett 38 pp 1103– (1977)
[9] Ablowitz, Non-linear evolution equations and ordinary differential-equations of Painlevé type, Lett. Nuovo Cimento 23 pp 333– (1978)
[10] Ablowitz, The generalized Chazy equation from the self-duality equations, Stud. Appl. Math 103 pp 75– (1999) · Zbl 1136.34301
[11] Fokas, The inverse scattering transform for the Benjamin-Ono equation - A pivot to multidimensional problems, Stud. Appl. Math 68 pp 1– (1983) · Zbl 0505.76031
[12] Fokas, On the inverse scattering of the time-dependent Schrödinger equation and the associated Kadomtsev-Petviashvili equation, Stud. Appl. Math 69 pp 211– (1983) · Zbl 0528.35079
[13] Fokas, Method of solution for a class of multidimensional non-linear evolution equations, Phys. Rev. Lett 51 pp 7– (1983)
[14] Herbst, Numerically induced chaos in the nonlinear Schrödinger equation, Phys. Rev. Lett 62 pp 2065– (1989)
[15] Ablowitz, Numerical chaos, roundoff errors, and homoclinic manifolds, Phys. Rev. Lett 71 pp 2683– (1993)
[16] Ablowitz, Coherent pulse propagation: A dispersive, irreversible phenomenon, J. Math. Phys 11 pp 1852– (1974)
[17] Ablowitz, Four-wave mixing in wavelength-division multiplexed soliton systems: damping and amplification, Opt. Lett 21 pp 1646– (1996)
[18] Ablowitz, On timing jitter in wavelength-division multiplexed soliton systems, Opt. Commun 150 pp 305– (1998)
[19] Ablowitz, Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems, Opt. Lett 25 pp 1750– (2000)
[20] Ablowitz, Nonlinear effects in quasi-linear dipersion-managed pulse transmission, IEEE Phot. Tech. Lett 13 pp 1082– (2001)
[21] Ablowitz, Multiscale dynamics in communication systems with strong dispersion management, Opt. Lett 23 pp 1668– (1998)
[22] Ablowitz, Quasi-linear optical pulses in dispersion-managed transmission systems, Opt. Lett 26 pp 459– (2001)
[23] Ablowitz, Spectral renormalization method for computing self-localized solutions to nonlinear systems, Opt. Lett 30 pp 2140– (2005)
[24] Ablowitz, On a new non-local formulation of water waves, J. Fluid Mech 562 pp 313– (2006) · Zbl 1098.76013
[25] Ablowitz, Carrier-envelope phase slip of ultrashort dispersion- managed solitons, Opt. Lett 29 pp 1808– (2004)
[26] Ablowitz, Asymptotic analysis of pulse dynamics in mode-locked lasers, Stud. Appl. Math 122 pp 411– (2009) · Zbl 1175.37072
[27] Ablowitz, Discrete diffraction-managed spatial solitons, Phys. Rev. Lett 87 pp 254102– (2001)
[28] Ablowitz, Nonlinear diffraction in photonic graphene, Opt. Lett 36 pp 3762– (2011)
[29] Hoefer, Piston dispersive shock wave problem, Phys. Rev. Lett 100 pp 084504– (2008)
[30] Ablowitz, Solitons and the Inverse Scattering Transform (1981)
[31] Ablowitz, Solitons, Nonlinear Evolution Equations and Inverse Scattering (1991)
[32] Ablowitz, Discrete and Continuous Nonlinear Schrödinger Systems (2004) · Zbl 1057.35058
[33] Ablowitz, Nonlinear dispersive waves (2011)
[34] Grinevich, Nonlocality and the inverse scattering transform for the Pavlov equation, Stud. Appl. Math 137 pp 10– (2016) · Zbl 1344.35126
[35] Prinari, Inverse scattering transform for the focusing Ablowitz-Ladik system with nonzero boundary conditions, Stud. Appl. Math 137 pp 28– (2016) · Zbl 1346.35174
[36] Miller, Direct scattering for the BenjaminOno equation with rational initial data, Stud. Appl. Math 137 pp 53– (2016) · Zbl 1346.35163
[37] Martin, Toward a general solution of the three-wave partial differential equations, Stud. Appl. Math 137 pp 70– (2016) · Zbl 1346.35192
[38] Clarkson, On Airy solutions of the second Painlevé equation, Stud. Appl. Math 137 pp 93– (2016) · Zbl 1346.35179
[39] Benincasa, Bianchi permutability for the antiselfdual Yang-Mills equations, Stud. Appl. Math 137 pp 110– (2016) · Zbl 1346.35169
[40] Calogero, New solvable variants of the goldfish manybody problem, Stud. Appl. Math 137 pp 123– (2016) · Zbl 1373.70008
[41] Sheils, Initial-to-interface maps for the heat equation on composite domains, Stud. Appl. Math 137 pp 140– (2016) · Zbl 1346.35195
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