Journal ArticleDOI
Method for solving the Korteweg-deVries equation
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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 asAbstract:
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 $|x|\ensuremath{\rightarrow}\ensuremath{\infty}$. The method can be used to predict exactly the "solitons," or solitary waves, which emerge from arbitrary initial conditions. Solutions that describe any finite number of solitons in interaction can be expressed in closed form.read more
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Journal ArticleDOI
New exact solutions to the mKdV equation with variable coefficients
TL;DR: In this paper, the variable-coefficient generalized projected Ricatti equation expansion method was used to find explicit solutions of the mKDV equation with variable coefficients, including solitary wave solutions, soliton-like solutions and trigonometric function solutions.
Journal ArticleDOI
Non‐self‐adjoint Zakharov–Shabat operator with a potential of the finite asymptotic values. I. Direct spectral and scattering problems
Naruyoshi Asano,Yusuke Kato +1 more
TL;DR: In this paper, the authors studied the Zakharov and Shabat equation for the scattering problem and showed that it yields a non-self-adjoint spectral operator in the Hilbert space in the sense of Dunford and Schwartz.
Journal ArticleDOI
Wakes and precursor soliton excitations by a moving charged object in a plasma
Sanat Kumar Tiwari,Abhijit Sen +1 more
TL;DR: In this article, the authors studied the evolution of nonlinear ion acoustic wave excitations due to a moving charged source in a plasma and showed the existence of a rich variety of solutions including wakes, precursor solitons, and "pinned" soliton that travel with the source velocity.
Journal ArticleDOI
Primitive potentials and bounded solutions of the KdV equation
Sergey A. Dyachenko,Dmitry Zakharov,Vladimir E. Zakharov,Vladimir E. Zakharov,Vladimir E. Zakharov +4 more
TL;DR: In this article, a broad class of bounded potentials of the one-dimensional Schrodinger operator, called primitive potentials, are constructed as solutions of a system of singular integral equations, which can be efficiently solved numerically.
Journal ArticleDOI
Noncommutative Extension of \bar∂-Dressing Method
Ning Wang,Ning Wang,Miki Wadati +2 more
TL;DR: In this paper, a non-commutative soliton equation and its Lax operators can be represented in the forms of Moyal product, the operator (functional of creation-annihilation operators) and the kernel function of the operator in coherent state representation (CSR).
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