Lie Symmetries, Conservation Laws and Exact Solutions for Jaulent-Miodek Equations

Pei, Jian-Ting; Bai, Yun

doi:10.3390/sym11101319

Cited by 3 publications

(1 citation statement)

References 29 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In previous studies, scientists investigated analytical solutions of Jaulent-Miodek equations in different forms and obtained a kink-type soliton, periodic-type soliton and bell-type soliton [54][55][56]. In addition, the following recent studies should be mentioned: Mbusi et al investigated the the exact solutions and conservation laws of a generalized (1+2)-dimensional JME with power-law nonlinearity [57]; Motsepa et al investigated the conservation law and gained the traveling wave solutions of the (2+1)-JME [58]; Gu utilized the complex method in order to obtain the exact solutions of the (2+1)-dimensional JME [45]; Iqbal et al studied the JM system with the modified exponential rational function method [59]; Guiping et al derived the new solitary solutions to the time-fractional coupled JME [60]; Sadat and Kassem gained explicit solutions for the (2+1) JME using the integrating factors method in an unbounded domain [61]; Kaewta et al studied the (2+1) conformable time partial integrodifferential JM equation using the exp-function [62] and transformed the (2+1)-dimensional JME into a fourth-order partial differential equation by having the exact solution [63]; Pei and Bai investigated the Lie symmetries, conservation laws and exact solutions for JME [64]. Furthermore, the space-time fractional form of the coupled JME by Chao and Qilong [65], the JME with positive dispersion by Jing et al [66] and dozens of other studies like these can be listed as studies emphasizing the importance of the JM equation.…”

Section: Introductionmentioning

confidence: 99%

Kink Soliton Dynamic of the (2+1)-Dimensional Integro-Differential Jaulent–Miodek Equation via a Couple of Integration Techniques

2023

View full text Add to dashboard Cite

In this article, the aim was to obtain kink soliton solutions of the (2+1)-dimensional integro-differential Jaulent–Miodek equation (IDJME), which is a prominent model related to energy-dependent Schrödinger potential and is used in fluid dynamics, condensed matter physics, optics and many engineering systems. The IDJME is created depending on the parameters and with constant coefficients, and two efficient methods, the generalized Kudryashov and a sub-version of an auxiliary equation method, were applied for the first time. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals ∂∂x,∂∂y and ∂∂t, was applied, and a nonlinear ordinary differential equation (NODE) form was derived. In order to make physical interpretations, appropriate solution sets and soliton solutions were obtained by performing systematic operations in line with the algorithm of the proposed methods. Then, 3D, 2D and contour simulations were made. Interpretations of different kink soliton solutions were made by obtaining results that are consistent with previous studies in the literature. The obtained results contribute to the studies in this field, though the contribution is small.

show abstract