A Study of an Extended Generalized (2+1)-dimensional Jaulent–Miodek Equation

Abstract

This paper aims to study the extended generalized (2+1)-dimensional Jaulent–Miodek equation (egJM), which arises in a number of significant nonlinear problems of physics and applied mathematics. We derive conservation laws using Noether theorem and find travelling wave solution of the egJM equation.

On optimal system, exact solutions and conservation laws of the modified equal-width equation

“…In this subsection we derive conservation laws for the modified equal-width equation (1) using Noether's theorem [18,19]. This equation as it is does not have a Lagrangian.…”

Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type system

“…Nonlinear partial differential equations (NLPDEs) have rapidly become indispensable in the quest to conceptualise the world around us [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] . We give a few recent studies of NLPDEs presented in the literature.…”

“…A great deal of useful mathematical models of natural phenomena do not have a variational principle. It is against this backdrop that in recent times astute mathematicians have sought a generalisation of Noether’s theorem with the intent of incorporating PDEs with or without a variational principle [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , [49] , [50] , [51] . One such generalisation is the aptly named multiplier approach [15] .…”

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

“…This fact was established by Emmy Noether, a German mathematician, in 1918 and is stated in Noether's theorem. For more details, see for example [34][35][36][37][38][39][40][41][42][43][44][45] and the references therein.…”