Approximate nonlinear self-adjointness and approximate conservation laws

Abstract

In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed by means of the method. As an application, a class of perturbed nonlinear wave equations is considered to illustrate the effectiveness.

13 pages, 2 tables

References in corpus (1)

• New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order

Cited by in corpus (3)

• Nonlinear Boundary Conditions for Energy and Entropy Stable Initial Boundary Value Problems in Computational Fluid Dynamics
• Nonlinear and Linearised Primal and Dual Initial Boundary Value Problems: When are they Bounded? How are they Connected?
• Approximate conditions admitted by classes of the Lagrangian $\mathcal{L}=\frac{1}{2}\left(-u^{\prime 2}+u^2\right)+{\epsilon }^i{G}_i(u,u^{\prime },u^{\prime \prime })$