Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On symmetries and conservation laws of a Gardner equation involving arbitrary functions

Rafael de la Rosa, María Luz Gandarias, María de los Santos Bruzón

TL;DR

This work studies a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations and constructs conservation laws by using Ibragimov theorem, based on the concept of adjoint equation for nonlinear differential equations.

Abstract

In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does not require the use of a variational principle. We also construct conservation laws using Ibragimov theorem which is based on the concept of adjoint equation for nonlinear differential equations.

On symmetries and conservation laws of a Gardner equation involving arbitrary functions

TL;DR

This work studies a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations and constructs conservation laws by using Ibragimov theorem, based on the concept of adjoint equation for nonlinear differential equations.

Abstract

In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does not require the use of a variational principle. We also construct conservation laws using Ibragimov theorem which is based on the concept of adjoint equation for nonlinear differential equations.
Paper Structure (7 sections, 3 theorems, 91 equations)

This paper contains 7 sections, 3 theorems, 91 equations.

Table of Contents

  1. Introduction
  2. Classical Symmetries
  3. Formal Lagrangian and adjoint equation
  4. Nonlinearly self-adjoint equations
  5. Conservation Laws
  6. Conservation laws by using the direct method of the multipliers of Anco and Bluman
  7. Conservation laws by using a general theorem on conservation laws proved by Ibragimov

Key Result

Theorem 1

The adjoint equation to equation (ed1) is

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Theorem 3