Abstract
Abstract. Based on Lieis symmetry approach, conservation laws are constructed for Fokas-Olver-Rosenau-Qiao(FORQ) equation and exact solution is obtained. Nonlocal conservation theorem is used to carry out the analysis of conservation process. Nonlinear self adjointness concept is applied to FORQ equation, it is proved to be strict self adjoint. Characteristic equation and similarity variable help us fnd exact solution of FORQ equation. Compared with solutions found in previous papers, our solution is new and important, since it is not possible to fnd exact solution of FORQ equation quite easily
Highlights
IntroductionMore works has been conducted on conservation laws
In recently past years, more works has been conducted on conservation laws
Based on Lie’s symmetry approach, conservation laws are constructed for Fokas–Olver–Rosenau–Qiao(FORQ) equation and exact solution is obtained
Summary
More works has been conducted on conservation laws. The determination of conservation laws, local ones, o¤ers rich knowledge on the mechanism of physical phenomena modeled by nonlinear evolution equations. An e¤ective and impressive way of constructing conservation laws is by means of well known Noether’s theorem [1]. This theorem provides explicit formulae for construction conservation laws for Euler-Lagrange di¤erential equations once their Noether symmetries are known. There has been an increasing interest in integrable non-evolutionary partial di¤erential equation of the form. Conservation laws, symmetry generators, FORQ equation, self adjointness, exact solution. Taking w = '(x; t; u); the construction of nonlinear self adjointness and conservation laws of the FORQ equation is presented. Using the similarity variables and reduced equation, exact solution is obtained
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