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Compacton and periodic wave solutions of the non-linear dispersive Zakharov-Kuznetsov equation

100%
|
EN
In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the sine-cosine method. As a result, compactons, periodic, and singular periodic wave solutions are found.
2
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Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

76%
Özdemir N., Yavuz M.
Acta Physica Polonica A
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2017
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vol. 132
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issue 3
1050-1053
EN
In this study, a new application of multivariate Padé approximation method has been used for solving European vanilla call option pricing problem. Padé polynomials have occurred for the fractional Black-Scholes equation, according to the relations of "smaller than", or "greater than", between stock price and exercise price of the option. Using these polynomials, we have applied the multivariate Padé approximation method to our fractional equation and we have calculated numerical solutions of fractional Black-Scholes equation for both of two situations. The obtained results show that the multivariate Padé approximation is a very quick and accurate method for fractional Black-Scholes equation. The fractional derivative is understood in the Caputo sense.
3
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Solutions of the perturbed KdV equation for convecting fluids by factorizations

76%
Cornejo-Pérez O., Rosu H.
Open Physics
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2010
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vol. 8
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issue 4
523-526
EN
In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential andWeierstrass functions.
4
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Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

76%
Wang C.-Y., Gui Y.-X., Gao Y.-J.
Open Physics
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2008
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vol. 6
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issue 3
462-468
EN
We present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.
5
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Inverse scattering method and soliton double solution family for string effective action

64%
Gao Y.-J.
Open Physics
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2009
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vol. 7
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issue 4
821-828
EN
A so-called modified Hauser-Ernst-type extended double-complex linear system is established and used to develop a new inverse scattering method for solving the equations of motion of the string effective action describing the coupled gravity, dilaton and Kalb-Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the application of the inverse scattering method fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.
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