Related papers: Nonlinear self-adjointness in constructing conserv…
Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a…
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, using the theory of Lie point symmetries of difference…
We study the nonlinear wave equation for arbitrary function with fourth order dissipation. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth…
In classical continuum mechanics, quasi-linear systems of conservation laws can be symmetrized if they admit an additional convex conservation law. In particular, this implies the hyperbolicity of governing equations. For capillary fluids,…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
A method based on infinite parameter conservation laws is described to factor linear differential operators out of nonlinear partial differential equations (PDEs) or out of differential consequences of nonlinear PDEs. This includes a…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…
We determine the Lie point symmetries of a class of BBM-KdV systems and establish its nonlinear self-adjointness. We then construct conservation laws via Ibragimov's Theorem.
We prove compactness and hence existence for solutions to a class of non linear transport equations. The corresponding models combine the features of linear transport equations and scalar conservation laws. We introduce a new method which…
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…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
Quasi-Noether differential systems are more general than variational systems and are quite common in mathematical physics. They include practically all differential systems of interest, at least those that have conservation laws. In this…
This paper is concerned with formally self-adjoint difference equations and their positive and negative deficiency indices. It is shown that the order of any formally self-adjoint difference equation is even, and some characterizations of…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
Using the maximal Lie algebra of point symmetries of a system of nonlinear equations used in geophysical fluid dynamics, two conservation laws are found in addition to the conservation of energy.
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
A nonlinear Lorentz invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian…
A method for constructing distributions on the non negative integers as discrete analogue of continuous distributions on the non negative real is presented. A justification of the definition of discrete self decomposable laws is provided.…
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…