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Solutions of the perturbed KdV equation for convecting fluids by factorizations

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Cornejo-Pérez O., Rosu H.

Open Physics

2010

vol. 8

issue 4

523-526

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.

Solution of a Class of Optimization Problems Based on Hyperbolic Penalty Dynamic Framework

100%

Evirgen F.

Acta Physica Polonica A

2017

vol. 132

issue 3

1062-1065

In this study, a gradient-based dynamic system is constructed in order to solve a certain class of optimization problems. For this purpose, the hyperbolic penalty function is used. Firstly, the constrained optimization problem is replaced with an equivalent unconstrained optimization problem via the hyperbolic penalty function. Thereafter, the nonlinear dynamic model is defined by using the derivative of the unconstrained optimization problem with respect to decision variables. To solve the resulting differential system, a steepest descent search technique is used. Finally, some numerical examples are presented for illustrating the performance of the nonlinear hyperbolic penalty dynamic system.

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1 Acta Physica Polonica A

1 Open Physics

1 2017

1 2010

1 Cornejo-Pérez O.

1 Evirgen F.

1 Rosu H.

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Solutions of the perturbed KdV equation for convecting fluids by factorizations

Solution of a Class of Optimization Problems Based on Hyperbolic Penalty Dynamic Framework