Ablowitz, Mark J.; Segur, Harvey Solitons and the inverse scattering transform. (English) Zbl 0472.35002 SIAM Studies in Applied Mathematics, 4. Philadelphia: SIAM - Society for Industrial and Applied Mathematics. X, 425 p. $ 54.50 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 1268 Documents MSC: 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35P25 Scattering theory for PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations 35J10 Schrödinger operator, Schrödinger equation 76B25 Solitary waves for incompressible inviscid fluids Keywords:inverse scattering transform; solitons; Korteweg-de Vries equation; nonlinear evolution equation; difference equations; periodic boundary conditions; Bäcklund transformations; Hirota’s method; Painleve property; fixed singularities; Sine-Gordon equations; Fourier transform method; nonlinear wave theory × Cite Format Result Cite Review PDF Full Text: DOI Digital Library of Mathematical Functions: §21.9 Integrable Equations ‣ Applications ‣ Chapter 21 Multidimensional Theta Functions §21.9 Integrable Equations ‣ Applications ‣ Chapter 21 Multidimensional Theta Functions §32.5 Integral Equations ‣ Properties ‣ Chapter 32 Painlevé Transcendents §9.16 Physical Applications ‣ Applications ‣ Chapter 9 Airy and Related Functions Profile Mark J. Ablowitz ‣ About the Project