• Corpus ID: 237213440

Complete Classification of Local Conservation Laws for Generalized Kuramoto-Sivashinsky Equation

  title={Complete Classification of Local Conservation Laws for Generalized Kuramoto-Sivashinsky Equation},
  author={Pavel Holba},
  • P. Holba
  • Published 19 August 2021
  • Mathematics
For an arbitrary number of spatial independent variables we present a complete list of cases when the generalized Kuramoto–Sivashinsky equation admits nontrivial local conservation laws of any order, and for each of those cases we give an explicit form of all the local conservation laws of all orders modulo trivial ones admitted by the equation under study. Introduction In the present paper we study the generalized Kuramoto–Sivashinsky equation, a PDE in n + 1 independent variables t, x1… 



Conservation laws for multidimensional systems and related linear algebra problems

We consider multidimensional systems of PDEs of generalized evolution form with $t$-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order

New exact solutions and conservation laws of a class of Kuramoto Sivashinsky (KS) equations

Abstract Lie symmetry method is used to perform detailed analysis on a class of KS equations. It is shown that the Lie algebra of the equation spanned by the vector fields of dilations in time and

Generalized symmetries and conservation laws of (1 + 1)-dimensional Klein–Gordon equation

Using advantages of nonstandard computational techniques based on the light-cone variables, we explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein-Gordon equation.

Lie symmetries and conservation laws for a generalized Kuramoto‐Sivashinsky equation

Nonlinear partial differential equations are used to describe complex phenomena in various fields of science. In this work, we consider a generalized fourth‐order nonlinear wave equation from the

The route to chaos for the Kuramoto-Sivashinsky equation

We present the results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. Our concern is with the asymptotic nonlinear dynamics