Journal ArticleDOI
The Three-Wave Interaction—A Nondispersive Phenomenon
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This article is published in Studies in Applied Mathematics.The article was published on 1976-03-01. It has received 220 citations till now.read more
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New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation
Narimasa Sasa,Junkichi Satsuma +1 more
TL;DR: In this paper, it was shown that a higher-order nonlinear Schrodinger equation which describes propagation of pulses in optical fiber is solvable by means of the inverse scattering transform, which possesses a remarkable property that it can propagate steadily with two peaks of the same height.
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On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψxxx + 6Qψx + 6Rψ = λψ
TL;DR: In this paper, the inverse scattering problem for cubic eigenvalue equations of the form ψxxx + 6Qψx + 6Rψ = λψ is outlined and formally solved.
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Formation and Interaction of Sonic-Langmuir Solitons Inverse Scattering Method
Nobuo Yajima,Masayuki Oikawa +1 more
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Resonantly interacting solitary waves
TL;DR: In this article, the phase-locked interactions between three obliquely oriented solitary waves are studied and it is shown that such interactions are associated with the parametric end points of the singular regime for interactions between two solitary waves.
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Recursion Operators and Bi-Hamiltonian Structures in Multidimensions. II
TL;DR: In this article, the authors present the general theory associated with recursion operators for bi-Hamiltonian equations in two spatial and one temporal dimensions, and show that general classes of equations, which include the Kadomtsev-Petviashvili and the Davey-Stewartson equations, possess infinitely many commuting symmetries and infinitely many constants of motion under two distinct Poisson brackets.
References
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Method for solving the Korteweg-deVries equation
TL;DR: In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as
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Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
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The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
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On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory
TL;DR: In this article, the energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method.
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Nonlinear-evolution equations of physical significance
TL;DR: In this article, the inverse scattering method was used to solve the initial value problem for a broad class of nonlinear evolution equations, including sine-Gordon, sinh-Gordon and Benney-Newell.