A brief historical introduction to solitons and the inverse scattering transform–a vision of Scott Russell

DOI10.1080/00207390600597849zbMath1358.35006OpenAlexW2079803322WikidataQ99705508 ScholiaQ99705508MaRDI QIDQ3499203

Lokenath Debnath

Publication date: 28 May 2008

Published in: International Journal of Mathematical Education in Science and Technology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207390600597849

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) History of mathematics in the 19th century (01A55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) History of partial differential equations (35-03) Soliton solutions (35C08) History of dynamical systems and ergodic theory (37-03)

Related Items (1)

Solitons and lump waves to the elliptic cylindrical Kadomtsev-Petviashvili equation

Cites Work

• Existence of breathers on FPU lattices
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
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• Korteweg‐devries equation and generalizations. VI. methods for exact solution
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• On the existence of a wave of greatest height and Stokes’s conjecture
• On the existence theory for irrotational water waves
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• Compactons: Solitons with finite wavelength
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Integrals of nonlinear equations of evolution and solitary waves
• Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices
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