Time-discretization of soliton
                    equations

Hirota, Ryoga; Iwao, Masataka

doi:10.1090/crmp/025/21

Cited by 29 publications

(21 citation statements)

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“…Hybrid Latticeu n (t) = (1 + αu n + βu 2 n )(u n−1 − u n+1 ) [17] u n (t) = −α± Table 2 Examples of DDEs and their solutions computed with DDESpecialSolutions.m.…”

Section: Relativistic Toda Latticeumentioning

confidence: 99%

Symbolic computation of hyperbolic tangent solutions for nonlinear differential–difference equations

Baldwin

Göktaş

Hereman

2004

Computer Physics Communications

148

113

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A new algorithm is presented to find exact traveling wave solutions of differentialdifference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh.Examples illustrate the key steps of the algorithm. Parallels are drawn through discussion and example to the tanh-method for partial differential equations.The new algorithm is implemented in Mathematica. The package DDESpecialSolutions.m can be used to automatically compute traveling wave solutions of nonlinear polynomial differential-difference equations. Use of the package, implementation issues, scope, and limitations of the software are addressed. Program summary

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“…Hybrid Latticeu n (t) = (1 + αu n + βu 2 n )(u n−1 − u n+1 ) [17] u n (t) = −α± Table 2 Examples of DDEs and their solutions computed with DDESpecialSolutions.m.…”

Section: Relativistic Toda Latticeumentioning

confidence: 99%

Symbolic computation of hyperbolic tangent solutions for nonlinear differential–difference equations

Baldwin

Göktaş

Hereman

2004

Computer Physics Communications

148

113

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“…The Volterra type equations are discretizations of the Kortewegde Vries (KdV) and modified KdV equations [26,27]. The exact solutions of (1) have been obtained by the tanh method [28].…”

Section: Optimal Ham For Volterra Latticementioning

confidence: 99%

Travelling-Wave Solution of Volterra Lattice by the Optimal Homotopy Analysis Method

Wang

2012

Zeitschrift Für Naturforschung A

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The travelling-wave solution of the Volterra lattice has been constructed by the optimal homotopy analysis method. The optimal method used here contains three auxiliary convergence-control parameters to adjust and control the convergence region of the solution. By minimizing the averaged residual error, the optimal convergence-control parameters can be obtained, which give much better approximations than those given by the usual homotopy analysis method. The obtained results show that the optimal homotopy analysis method is also very efficient for differential-difference equations.

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“…B. Diaz and T. J. Osler [7] defined the fractional difference by the rather natural approach of allowing the index of differencing, in the standard expression for the n th difference, to be any real or complex number. Later, R. Hirota [9], defined the fractional order difference operator ∇ α where α is any real number, using Taylor's series. A. Nagai [10] adopted another definition for fractional difference by modifying Hirota's definition.…”

Section: Introductionmentioning

confidence: 99%