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

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.

Conservation Laws and Explicit Solution of system of Fractional-Order Coupled Nonlinear Hirota Equations by Lie Symmetry Analysis

“…Noether's theorem [27,31,33] established a relation between conservation laws and symmetry of differential equations and applied on FPDEs without Lagrangian operators. Recently, authors [34,[36][37][38][39]47] provided invariance structure, explicit exactsolutions with power series solution and conservation analysis of Boussinesq-Burger's system, Drinfeld-Sokolov-Satsuma-Hirota coupled KdV and m-KdV equations via Lie symmetry analysis. Biswas et al [12][13][14] have worked on dual dispersion, power laws, conservation laws and optimal quasi-solitons by Lie symmetry analysis.…”

On obtaining analytical soliton solutions of Drinfeld-Sokolov-Satsuma-Hirota equation via two efficient methods

“…Furthermore, in the study denoted by [27], a Darboux transformation applicable to the DSSH system was developed. The analytical solutions for the DSSH system were derived using a synthesis of Lie symmetry analysis, simplest equation method, and Jacobi elliptic function approaches, as detailed in [28,29]. In [30], the authors extracted explicit solutions.…”

Conservation laws and exact series solution of fractional‐order Hirota–Satsuma‐coupled Korteveg–de Vries system by symmetry analysis

“…The Lie symmetry invariant analysis and conservation laws have made progress in FPDEs; still, the research field for coupled KdV fractional‐order system is not well exposed. This system was proposed by Hirota and Satsuma to describe the relation between long waves with distinct dispersion interactions, and its generalized behavior has led to relevance in various branches of applied mathematics and time‐fractional Hirota–Satsuma‐coupled (HSC)‐KdV system has been studied by using various methods 46–49 . The focus of this article is to investigate fractional order Lie symmetry analysis and new conservation laws via Noether's theorem for coupled time‐fractional HSC‐KdV system 33 of fractional parameter θ .…”