On the solutions and conservation laws of the coupled Drinfeld-Sokolov-Satsuma-Hirota system

Khadijo Rashid Adem; Chaudry Masood Khalique

doi:10.1186/s13661-014-0248-6

On the solutions and conservation laws of the coupled Drinfeld-Sokolov-Satsuma-Hirota system

Khadijo Rashid Adem, Chaudry Masood Khalique^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

In this paper we study the coupled Drinfeld-Sokolov-Satsuma-Hirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a special form. Also this system was found as a special case of the four-reduction of the Kadomtsev-Petviashivilli hierarchy. We obtain exact solutions of the system by using Lie symmetry analysis along with the simplest equation and Jacobi elliptic equation methods. Also, symmetry reductions are obtained based on the optimal system of one-dimensional subalgebras. In addition, the conservation laws are derived using two approaches: the new conservation theorem due to Ibragimov and the multiplier method.

Original language	English
Article number	248
Journal	Boundary Value Problems
Volume	2014
Issue number	1
DOIs	https://doi.org/10.1186/s13661-014-0248-6
Publication status	Published - 2014
Externally published	Yes

Keywords

Jacobi elliptic function method
Lie symmetry methods
conservation laws
coupled Drinfeld-Sokolov-Satsuma-Hirota system
simplest equation method

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10.1186/s13661-014-0248-6

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abstract = "In this paper we study the coupled Drinfeld-Sokolov-Satsuma-Hirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a special form. Also this system was found as a special case of the four-reduction of the Kadomtsev-Petviashivilli hierarchy. We obtain exact solutions of the system by using Lie symmetry analysis along with the simplest equation and Jacobi elliptic equation methods. Also, symmetry reductions are obtained based on the optimal system of one-dimensional subalgebras. In addition, the conservation laws are derived using two approaches: the new conservation theorem due to Ibragimov and the multiplier method.",

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AU - Adem, Khadijo Rashid

AU - Khalique, Chaudry Masood

PY - 2014

Y1 - 2014

N2 - In this paper we study the coupled Drinfeld-Sokolov-Satsuma-Hirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a special form. Also this system was found as a special case of the four-reduction of the Kadomtsev-Petviashivilli hierarchy. We obtain exact solutions of the system by using Lie symmetry analysis along with the simplest equation and Jacobi elliptic equation methods. Also, symmetry reductions are obtained based on the optimal system of one-dimensional subalgebras. In addition, the conservation laws are derived using two approaches: the new conservation theorem due to Ibragimov and the multiplier method.

AB - In this paper we study the coupled Drinfeld-Sokolov-Satsuma-Hirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a special form. Also this system was found as a special case of the four-reduction of the Kadomtsev-Petviashivilli hierarchy. We obtain exact solutions of the system by using Lie symmetry analysis along with the simplest equation and Jacobi elliptic equation methods. Also, symmetry reductions are obtained based on the optimal system of one-dimensional subalgebras. In addition, the conservation laws are derived using two approaches: the new conservation theorem due to Ibragimov and the multiplier method.

KW - Jacobi elliptic function method

KW - Lie symmetry methods

KW - conservation laws

KW - coupled Drinfeld-Sokolov-Satsuma-Hirota system

KW - simplest equation method

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SN - 1687-2762

VL - 2014

JO - Boundary Value Problems

JF - Boundary Value Problems

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ER -

On the solutions and conservation laws of the coupled Drinfeld-Sokolov-Satsuma-Hirota system

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