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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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Generalized Wronskian relations, one-dimensional Schrödinger equation and nonlinear partial differential equations solvable by the inverse-scattering method
TL;DR: In this paper, a generalized Wronskian-type relation is used to obtain a number of expressions for the scattering and bound state parameters (reflection and transmission coefficients, bound-state energies and normalization constants) in the context of the one-dimensional Schrodinger equation.
Journal ArticleDOI
A fourth order numerical scheme for the one-dimensional sine-Gordon equation
TL;DR: A numerical scheme arising from the use of a fourth order rational approximants to the matrix-exponential term in a three-time level recurrence relation is proposed for the numerical solution of the one-dimensional sine-Gordon (SG) equation already known from the bibliography.
A Comparison of Variational Iteration Method with Adomian's Decomposition Method in Some Highly Nonlinear Equations
TL;DR: In this article, equations of Generalized Hirota-Satsuma coupled KdV equation, Kawahara equation and FKdV equations are solved through variational iteration method and the results are compared with those of Adomian's decomposition method (ADM).
Posted Content
Dynamics of the sixth painlev ´ e equation
TL;DR: In this article, a complete picture of the 6 Painleve equation's dynamical nature based on the Riemann-Hilbert approach was given. But the authors restricted their analysis to the original 6 painleve equations.
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Symbolic computation on tunable nonautonomous solitons in inhomogeneous NLS system with generalized external potential
TL;DR: In this article, the propagation of optical solitons in a generalized nonautonomous nonlinear Schrodinger equation with more generalized external potential is investigated for different forms of variable coefficients which are important in the soliton control.
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