Forced Nonlinear Evolution Equations and the Inverse Scattering Transform

DOI10.1002/sapm1989803253zbMath0696.35135OpenAlexW2474473138MaRDI QIDQ3472555

Mark J. Ablowitz, Athanassios S. Fokas

Publication date: 1989

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1989803253

zbMATH Keywords

solitons nonlinear Schrödinger equations Korteweg-de Vries

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (38)

The nonlinear Schrödinger equation in the finite line ⋮ Global bifurcation theory for periodic traveling interfacial gravity-capillary waves ⋮ Solution of the forced nonlinear schrödinger (nls) equation using pde techniques ⋮ Efficient computation of highly oscillatory integrals with Hankel kernel ⋮ On integration of Korteweg-de Vries equation in a class of rapidly decreasing complex-valued functions ⋮ Forced solitary waves and hydraulic falls in two-layer flows ⋮ The Burgers equation under deterministic and stochastic forcing ⋮ Integrable Equations with a Forcing of a Distribution Type ⋮ Discrete matrix Riccati equations with superposition formulas ⋮ Nonlinear heat diffusion under impulsive forcing ⋮ Long-time asymptotic for the Hirota equation via nonlinear steepest descent method ⋮ A fast Chebyshev method for simulating flexible-wing propulsion ⋮ On linear systems and \(\tau\) functions associated with Lamé's equation and Painlevé's equation VI ⋮ Numerical approximations to integrals with a highly oscillatory Bessel kernel ⋮ Geometric phase within the complex quantum Hamilton-Jacobi formalism ⋮ Recalculation of the spectrum of the radiation emitted during gravitational collapse ⋮ Burgers equation in 2D \(\mathrm{SU}(N)\) YM ⋮ Phase-amplitude dynamics of the nonlinear Schrödinger equation with rapid forcing ⋮ The inverse scattering problem for the perturbed string equation and its application to integration of the two-dimensional generalization from Korteweg-de Vries equation ⋮ Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations ⋮ Unnamed Item ⋮ Arbitrary Lagrangian-Eulerian rate equation for the Born probability density in complex space ⋮ On a forced modified KdV equation. ⋮ An interpretation of absolutely and convectively unstable waves using series solutions ⋮ Global asymptotics of orthogonal polynomials associated with \(|x|^{2\alpha} e^{-Q(x)}\) ⋮ A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect ⋮ A simple similarity-transformation-iterative scheme applied to Korteweg-de Vries equation ⋮ The Cauchy problem of the Ward equation ⋮ Efficient method for the computation of oscillatory Bessel transform and Bessel Hilbert transform ⋮ The large-time development of the solution to an initial-boundary value problem for the Korteweg-de Vries equation. I: Steady state solutions ⋮ Growth estimates in the Hardy--Sobolev space of an annular domain with applications ⋮ Rational compacts and exposed quadratic irrationalities ⋮ Soliton generation for initial-boundary-value problems ⋮ A Riemann-Hilbert approach to the Laplace equation ⋮ On the Burgers equation with moving boundary ⋮ ON INTEGRATION OF THE LOADED KORTEWEG-DE VRIES EQUATION IN THE CLASS OF RAPIDLY DECREASING FUNCTIONS ⋮ Locally forced critical surface waves in channels of arbitrary cross section ⋮ The first exit time and ruin time for a risk process with reserve-dependent income.

Cites Work

This page was built for publication: Forced Nonlinear Evolution Equations and the Inverse Scattering Transform