Schlesinger transformations for the second members of PII and PIV hierarchies

In this paper, we give a method to obtain the Schlesinger transformations for the second members of second and fourth Painlev´e hierarchies. The procedure involves formulating a Riemann–Hilbert problem for a transformation matrix which transforms the solution of the linear problem but leaves the associated monodromy data the same.In this paper, we give a method to obtain the Schlesinger transformations for the second members of second and fourth Painlev´e hierarchies. The procedure involves formulating a Riemann–Hilbert problem for a transformation matrix which transforms the solution of the linear problem but leaves the associated monodromy data the same

On special solutions of second and fourth Painlevé hierarchies

In this article, we give special solutions of second and fourth Painlev´e hierarchies derived by Gordoa, Joshi, and Pickering. We show that for certain choice of the parameters each n-th member of these hierarchies has a special solution in terms of an n-th order differential equation. Furthermore we derive a relation between these two hierarchies.In this article, we give special solutions of second and fourth Painlev´e hierarchies derived by Gordoa, Joshi, and Pickering. We show that for certain choice of the parameters each n-th member of these hierarchies has a special solution in terms of an n-th order differential equation. Furthermore we derive a relation between these two hierarchies

Linear problems and hierarchies of Painlevé equations

In this paper, we show that the expansion of linear problems of the Painlev´e equation in powers of the spectral variable can be used to derive hierarchies of ordinary differential equations. We applied this approach to linear problems of the first, second, third and fourth Painlev´e equations. We derived a new hierarchy of the third Painlev´e equation and rederived known hierarchies of the other equations. Moreover some special solutions of the hierarchies of the second, third and fourth Painlev´e equations are also given.In this paper, we show that the expansion of linear problems of the Painlev´e equation in powers of the spectral variable can be used to derive hierarchies of ordinary differential equations. We applied this approach to linear problems of the first, second, third and fourth Painlev´e equations. We derived a new hierarchy of the third Painlev´e equation and rederived known hierarchies of the other equations. Moreover some special solutions of the hierarchies of the second, third and fourth Painlev´e equations are also given

B¨acklund transformations for Cosgrove’s equation F-XVIII

In this paper we study B¨acklund transformations (BTs) for Cosgrove’s equation F-XVIII.We use the generalization of Fokas and Ablowitz method to derive BTs between F-XVIII and new fourth-order ordinary differential equations (ODEs) of Painlev´e-type. Moreover we derive auto-BT and give special solutions for F-XVIII.In this paper we study B¨acklund transformations (BTs) for Cosgrove’s equation F-XVIII.We use the generalization of Fokas and Ablowitz method to derive BTs between F-XVIII and new fourth-order ordinary differential equations (ODEs) of Painlev´e-type. Moreover we derive auto-BT and give special solutions for F-XVII

First-order second-degree equations related with Painlevé equations

The first-order second-degree equations satisfying the Fuchs theorem concerning the absence of movable critical points, related with Painlev´e equations, and one-parameter families of solutions which solve the first-order second-degree equations are investigated.The first-order second-degree equations satisfying the Fuchs theorem concerning the absence of movable critical points, related with Painlev´e equations, and one-parameter families of solutions which solve the first-order second-degree equations are investigated

SYMMETRIES AND EXACT SOLUTIONS OF CONFORMABLE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

In this paper Lie group analysis is used to investigate invariance properties of nonlinear fractional partial differential equations with conformable fractional time derivative. The analysis is applied to Korteweg-de Vries, modified Korteweg-de Vries, Burgers, and modified Burgers equations. For each equation, all of the vector fields and the Lie symmetries are obtained. Moreover, exact solutions are given to these equations.In this paper Lie group analysis is used to investigate invariance properties of nonlinear fractional partial differential equations with conformable fractional time derivative. The analysis is applied to Korteweg-de Vries, modified Korteweg-de Vries, Burgers, and modified Burgers equations. For each equation, all of the vector fields and the Lie symmetries are obtained. Moreover, exact solutions are given to these equations

ON TAYLOR DIFFERENTIAL TRANSFORM METHOD FOR THE FIRST PAINLEVE EQUATION

We apply the Taylor Differential Transform Method (TDTM) to the initial value problem of the fi rst Painleve equation. We use the deviation to calculate the accuracy of the solutions and the results are compared with the known results. Four sets of initial values, two of them were not considered before, are considered to illustrate the effectiveness of the method.We apply the Taylor Differential Transform Method (TDTM) to the initial value problem of the fi rst Painleve equation. We use the deviation to calculate the accuracy of the solutions and the results are compared with the known results. Four sets of initial values, two of them were not considered before, are considered to illustrate the effectiveness of the method

Study of Shoreline Changes at Jeneberang River Delta, Makassar

The study of shoreline changes during 1990 - 2008 in the delta of the River Jeneberang, Makassar was conducted by evaluating sediment transport into and out of a cell. Longshore sediment transport was computed by considering the influence of heights and angles of the breaking waves. Results of calculation of sediment transport showed that the dominant of sediment transport was to the north during the arrival of the southwest and west waves, and to the south when the wave coming from the northwest. Comparison between shore profiles resulting from model and coastline satellite imagery showed similarity. The difference between the two tend to be occurred at the head land part of the shoreline. This was due to complexity of coastal dynamic at the area. The results of the 19 years shoreline simulation showed that there was a tendency of abrasion at the upsteam head land part as the wave energy tend to converge and accretion at the bay part as the wave energy tend to diverge. Abrasion mainly occurred at Tanjung Bunga (head land) where the coast retreat 181.1 m. Accretion occur in the bay area (Tanjung Merdeka) where the coast advance to the sea for about 59.8 m. The shoreline tend to be stable when the profile was straight such as Barombong Coast

Electrodeposition of platinum and silver into chemically modified microporous silicon electrodes

Electrodeposition of platinum and silver into hydrophobic and hydrophilic microporous silicon layers was investigated using chemically modified microporous silicon electrodes. Hydrophobic microporous silicon enhanced the electrodeposition of platinum in the porous layer. Meanwhile, hydrophilic one showed that platinum was hardly deposited within the porous layer, and a film of platinum on the top of the porous layer was observed. On the other hand, the electrodeposition of silver showed similar deposition behavior between these two chemically modified electrodes. It was also found that the electrodeposition of silver started at the pore opening and grew toward the pore bottom, while a uniform deposition from the pore bottom was observed in platinum electrodeposition. These electrodeposition behaviors are explained on the basis of the both effects, the difference in overpotential for metal deposition on silicon and on the deposited metal, and displacement deposition rate of metal