Solitons and the Inverse Scattering Transform

By Lokenath Debnath. 2012

1,404 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0fd673e34953d323609560a452e69fd223a5a25a

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

KP solitons in shallow water (2010, background): “For example, in the case π = (1 2 3 4 3 1 4 2), we have the [1, 3]- and [3, 4]-solitons in y 0 and the [1, 2]- and [2, 4]-solitons in y 0.”
Discrete Integrable Systems (2010, background): “Integrability is closely related to the Lax pairs, the Hamiltonian structure, infinitely many conservation laws, the backlund transformation, arbitrary number of soliton solutions, symmetry, Painleve property and so on [4-8].”
Dispersive shock waves and modulation theory (2016, result): “The IST approach was extended to non-decaying step-like initial conditions by Khruslov [110] who explained the apparent contradiction between the absence of discrete spectrum in the KdV step problem and the appearance of solitons at the DSW leading edge in the GP solution.”
Dark solitons in atomic Bose–Einstein condensates: from theory to experiments (2010, methodology): “Relevant mathematical tools, such as Inverse Scattering Transform (IST), the renormalization of the integrals of motion of dark solitons and the small-amplitude approximation — leading to the connection of matterwave dark solitons to Korteweg-de Vries (KdV) solitons — are discussed.”
Dispersion-managed solitons in fibre systems and lasers (2012, background): “It can be shown that the radiative part of the energy is dispersing and vanishing with propagation distance [3,12,25].”
Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions (2016, methodology): “Applications are diverse and include problems in fluid mechanics, electromagnetics, gravitational waves, elasticity, fundamental physics and lattice dynamics, to name but a few [4, 6, 8].”
Integrable nonlocal nonlinear Schrödinger equation. (2013, methodology): “—We begin our analysis by considering the following scattering problem [8,16]”
Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons (2010, background): “[14] and was elegantly formulated and developed in outstanding papers by Lax [48], Zakharov, Shabad, and Ablowitz, Kaup, Newell and Segur (AKNS) (see [49] and references therein).”
Existence of Solitary Waves and Periodic Waves to a Perturbed Generalized KdV Equation (2014, neutral): “There exists a lot of investigation on explicit and exact solitary wave solutions to the KdV equation, for instance, [2,8,9].”